I have no proof that Jeremiah had two wives, but given the age difference between Jeremiah and Emeline, we would immediately suspect he had an earlier wife.  The age of the eldest child also suggests that there may have been an earlier wife.

1.  Anon.  1966.  Marriage Index:  Ohio, 1789-1850.  Liahona Research, Orem, UT (Broderbund CD-400):

Gilles, Jeremiah

Bradley, Emmeline

10 Mar 1835

Delaware Co.

2.  1830 Census Index/Images (online at Ancestry.com; Image #1 of 8 — indexed "Jeremiah Giffis"; extracted by Diana Gale Matthiesen):

1830

OH

Delaware Co.

Liberty Twp.

p. 83

Ln. 14

Jerh Gillies

001 010 - 001 000 010

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	10-14	1815-1820	= Brother?
1 male	20-29	1800-1810	= Jeremiah (b. 1804/5)
1 female	10-14	1815-1820	= Sister?
1 female	50-59	1770-1780	= Widowed Mother?

Listed two lines from Jeremiah's apparent uncle, James GILLIS.  They are the only GILLISes in Delaware County.

3.  1840 Census Index/Images (online at Ancestry.com, Image #5 of 10; extracted by Diana Gale Matthiesen):¤

1840

OH

Delaware Co.

Liberty Twp.

pp. 127B-128A

Ln. 2

Jeremiah Gillis

110 001 - 000 010 001

0100000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	= Son B
1 male	5-9	1830-1835	= Son A
1 male	30-39	1800-1810	= Jeremiah (b. 1804/5)
1 female	20-29	1810-1820	= Emeline (b. 1815/6)
1 female	60-69	1770-1780	= Anna CARPENTER (b. 1775/6)
1	person employed in agriculture

4.  1850 Census Index/Images (online at Ancestry.com; Image #25 of 25):  Liberty Twp., Delaware Co., OH, p. 216A, 1624/1635, enumerated 17 Aug 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):¤

Jeremiah Gillis	45	M		Farmer		O
Emiline    "	34	F				O
Joseph     "	6	M				O
Emily      "	4	F				O
Anna Carpenter	74	F				Pa

Anna (CELLAR) CARPENTER is Jeremiah's aunt.

5.  1860 Census Index/Images (online at Genealogy.com, Image #14 of 30):  Dublin P.O. [in Franklin Co., OH], Liberty Twp., Delaware Co., OH, Roll 957 (Book 1), p. 221B, PN 14, 98/102, enumerated 6 Jun 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

Jeremiah Gillis	56	M		Town Clerk		150	O
Joseph	16	M					"
Emily	13	F					"
Romeo	7	M					"

6.  1870 Census Index/Images (online at Genealogy.com, Image #13 of 16):  Charloe P.O., Jackson Twp., Paulding Co., OH, Roll 1254 (Book 1), p. 537A, PN 13, 99/88, enumerated 19 Jun 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Gillis Jeremiah	68	M	W	Farmer	800		Ohio
______ Emily	23	F	W	Keeping House			Ohio
______ Romeo	16	M	W	At Home			Ohio

7.  1880 Census (indexed at FamilySearch.org):  not found.

8.  Monday, 13 Nov 1950.  "Obituaries."  The Marion Star (Marion, Ohio), v. LXXIII, n. 297, p. 10 (online at Ancestry.com).  Obituary of their son, Romeo GILLIS.