Building off of and in addition to the information uncovered by ColeValleyGirl, in the 1891 Chester Census, Joseph and Jane and their children live next door to what appear to be Jane's parents, Thomas and Jane Perry who are 63.
1891 Chester Census Info:
Joseph Campbell
Gender: Male
Age: 36
Relationship: Head
Birth Year: 1855
Spouse: Jane Ann Campbell
Child: James Campbell
Ann Elizabeth Campbell
Jane Campbell
Thomas Campbell
Birth Place: Cheshire, England
Civil Parish: Chester
Ecclesiastical parish: St Mary without the Walls
Residence Place: Chester, Cheshire, England
Registration district: Chester
Sub registration district: Chester Castle
ED, Institution or Vessel: 11
Neighbors: View others on page
Piece: 2862
Folio: 97
Household Members:
Name Age
Joseph Campbell 36
Jane Ann Campbell 34
James Campbell 10
Ann Elizabeth Campbell 9
Jane Campbell 6
Thomas Campbell 1
Also in addition, there is an entry in the 1881 Census for a young and married Joseph who is the master on a vessel in Bancroft:
I also found a baptism record (Cheshire, England, Select Bishop's Transcripts, 1576-1933):
Name: Joseph Campbell
Gender: Male
Baptism Date: 3 Dec 1854
Baptism Place: St. Mary's-on-the-Hill, Chester, Cheshire, England
Father: William Campbell
Mother: Ann
FHL Film Number: 1655537
The 1871 Census has an appropriately aged set of Joseph and his parents, if they're William and Ann, as suggested from the baptism record, but they're all born in Huntingdonshire instead of Chester, which is a bit far:
Name: William Campbell
Age: 39
Estimated birth year: abt 1832
Relation: Head
Spouse's Name: Ann Campbell
Gender: Male
Where born: Huntingdonshire, England
Civil Parish: All Saints
County/Island: Huntingdonshire
Country: England
Registration district: Huntingdon
Sub-registration district: Huntingdon
ED, institution, or vessel: 9
Household schedule number: 39
Piece: 1527
Folio: 11
Page Number: 13
Household Members:
Name Age
William Campbell 39
Ann Campbell 40
Joseph William Campbell 16
Frances Ann Campbell 14
Stephen Campbell 12
William James Campbell 10
John Campbell 8
Winifred Campbell 4
Emily Campbell 2
I'm not sure if any of this is helpful, but wanted to provide it just in case.