As the 1851 census is the Unfilmed one and i do not think is on Ancestry:

1851 census:
RG number: HO107
Piece: 2233
Folio: 0
Page: 0
Reg. District: Ashton under Lyne
Sub District: Ashton Town
Parish: Ashton-Under-Lyne
Enum. District:
Ecclesiastical District:
City/Municipal Borough:
Address: Hibberts Court, Ashton-Under-Lyne
County: Lancashire

MULHOLLAND, William Head Married M 33 1818 Carder Cotton
Ireland
MULHOLLAND, Mary Wife Married F 31 1820 Tenter Cotton
Ireland
MULHOLLAND, Mary Dau F 11 1840 Tenter Silk
Dukinfield, Cheshire
MULHOLLAND, Theresa Dau F 10 1841 Scholar
Dukinfield, Cheshire
MULHOLLAND, John Henry Son M 8 1843 At Home
Dukinfield, Cheshire
MULHOLLAND, Edward Son M 4 1847 Illegible
Dukinfield, Cheshire
MULHOLLAND, Bridget Dau F 2 1849 Illegible
Dukinfield, Cheshire
MULHOLLAND, Ambrose Son M 0 (3M) 1851 Illegible
Ashton U Lyne, Lancashire.

The transcript is bobbins see CheshireBMD for the childrens names and births:

http://www.cheshirebmd.org.uk/index.php

Both parents Mary and Bernard died before the 1871 census, Mary in 1864 and Bernard in 1869. The Ambrose in the 1851 also passed away before the 1861 being replaced by an Ambrose born 1859.

So from 1859 we are looking for Bernard born 1846, James born 1856 and Ambrose 1859, as well as Bernard and Mary


Marriage from Lancs OPC:

Marriage: 18 Dec 1837 St Michael and All Angels, Ashton under Lyne, Lancashire, England
Barney Mulholland - full age, Labourer, Bachelor, Town
Mary Reynolds - (X), full age, Spinster, Town
Groom's Father: Henry Mulholland, Tailor
Bride's Father: Henry Reynolds, Labourer
Witness: Thomas Grimshaw; William Armitage
Married by Banns by: Geoe. Wd. Bower
Register: Marriages 1837 - 1839, Page 59, Entry 117
Source: LDS Film 1550973