(Frederick) Henry DREISCHMEYER
Catherine ASHEMAN
Husband:  (Frederick) Heinrich / Henry DREISCHMEYER
Birth:  9 Aug 1840, Detmold, State of Lippe, Germanic Confederation [now part of the State of North Rhine-Westphalia]
Occupation:  farmer
Father:  Gustav DREISCHMEYER
Mother:  Wilemine __?__
Marriage:  23 Mar 1864, Santa Clara Co., CA
Wife:  Catharina / Catherine "Kate" ASHEMAN / ASHMAN / ASHERMAN / ACKERMAN / ASCHMANN
Birth:  1839/40, Kingdom of Hanover [now part of Lower Saxony]
Children — born in Santa Clara Co., CA:
1.  Henry DREISCHMEYER, b. 11 Jun 1864
2.  Frederick Aloysius "Fred" DREISCHMEYER, b. 1 Jan 1866 
3.  Lizzie DREISCHMEYER, b. 18 Nov 1867; d.s.p. 21 Oct 1868, CA
4.  Mary DREISCHMEYER, b. 22 Nov 1869
5.  William J. DREISCHMEYER, b. 21 May 1872, Gilroy 
6.  Frank L. DREISCHMEYER, b. 20 May 1874, Gilroy
Keywords for search engines:  Germany; USA, Illinois, California

Timeline
Year Location Event
1840 Germany: Lippe: Detmold birth of Henry DREISCHMEYER
1839/40 Germany: Hanover birth of Catherine ASHEMAN
1852/3 Germany to Chicago Henry's parents immigrate
1854   death of Henry's parents
1860 Census    
1864 CA: Santa Clara Co. marriage of Henry DREISCHMEYER to Catherine ASHEMAN
1864 CA birth of son, Henry
1866 CA birth of son, Fred
1867   birth of daughter, Lizzie
1868   death of daughter, Lizzie
1869 CA birth of daughter, Mary
1870 Census CA: Santa Clara Co.: Gilroy H. "DRESHMYER," head-of-household
1872 CA birth of son, William
1874 CA birth of son, Frank 
1880 Census CA: Santa Clara Co.: Gilroy H. DREISCHMEYER, head-of-household

Sources:

1.  Office of the Clerk Recorder, Santa Clara County, California. Marriage Certificates (database online at the official Santa Clara County, California, web site):
Dreischmeyer, Henry Achermann, Catherine 03/23/1864 Book B, p. 193 Cert. #6400193

2.  1860 Census Every-Name-Index/Images (online at Ancestry.com):  can't find, though he should be unmarried in in Chicago.

3.  1870 Census Images (online at Ancestry.com; Image #199 of 676):  Gilroy P.O., Gilroy Twp., Santa Clara Co., CA, p. 100A, PN 67, enumerated 25 July 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):
1870:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1 2 3 4 5 6 7 8 9 10 11 12 13 19
506 477 Dreshmyer H 29 M W Farmer 5000 1000 Germany / /   /
        "     Kate 30 F W Keeping House     Hanover / /    
        "     Henry  6 M W       California / /    
        "     Fred  4 M W       " / /    
        "     Mary 8/12 F W       " / / Nov  
        "     Fred 20 M W Laborer    100 Germany / /    
    Ashmon Fred 28 M W "    150 " / /    
    Core? Fred 27 M W "     50 " / /    
    Kick??? Jno? 24 M W "     " / /    
The 20-yr-old Fred DREISCHMEYER appears to be Henry's younger brother, just as Fred ASHMAN appears to be Catherine's younger brother.  I'm wondering if Fred DREISCHMEYER didn't accidentally get enumerated twice, once here, and once, seven weeks earlier, with the SCHLET family.  As an unmarried laborer, he could easily move about, and it wouldn't be the first time I've seen someone enumerated twice in the same census.  Otherwise, we've got two Fred DREISCHMEYERs, both born in 1850 in Germany and both living in Gilroy in 1870, which is possible if all the brothers have the same saint's name.

4.  1880 Census Microfilm Images (online at Ancestry.com):  Gilroy Twp. (outside of town), Santa Clara Co., CA, p. 410B, SD 1, ED 258, P# 30, enumerated 18 Jun 1880 (extracted by Diana Gale Matthiesen):
1880:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1 2 3 4 5 6 8 9 10 13 21 24 25 26
178 178 Dreischmeyer H. W M 40     / Farmer   Germany Germany Germany
    ____________ Catherine W F 40 Wife   / Keeping house   Hanover Hanover Hanover
    ____________ Henry W M 16 Son /   At home / Cal. Germany Hanover
    ____________ Frederick W M 14 Son /   At home / Cal. Germany Hanover
    ____________ Mary W F 10 Dau /   At home / Cal. Germany Hanover
    ____________ William W M  8 Son /     / Cal. Germany Hanover
    ____________ Frank W M  6 Son /     / Cal. Germany Hanover

5.  Anon. [Preface signed by J.P. Munro-Fraser].  1881. History of Santa Clara County, California.  Alley, Bowen & Co., San Francisco, CA (online at HeritageQuest at Genealogy.com):
p. 603 Henry Dreischmeyer.  Born in Lippe-Detmold Principality, Germany, August 9, 1840, and came to the United States in 1854, having received his education chiefly in his native land.  He first settled in Chicago, and resided there until 1863, when he came to California by way of the Nicaragua route, arriving in San Frnacisco, April 27th, of the same year.  He forthwith proceeded to, and located in, the town of Santa Clara, but at the end of
p. 604 two months he transferred his domicile to San José, and started as a brickmaker, an occupation he followed until he went to Gilroy, moving to his present farm in the year 1869.  Married, September, 1863, Catherine Asheman, a native of Germany, and has:  Henry, born June 11, 1864; Frederick, born January 1, 1866; Lizzie, born November 18, 1867, died October 21, 1868; May, born November 22, 1869; William, born May 20, 1872; Frank, born May 20, 1874.

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