lhyyym said:
If the husband is a student, while the wife stays at home to take care of babies without a job, could the wife apply for citizenship when she meets the resident requirements? If OK, how could the wife certify her residency without study or employment records in Canada?
Concurring with others, but yes, indeed, IRCC may request more proof from an applicant in this situation, one in which providing a paper trail of a life lived in Canada could be difficult.
Medical visits for the children, a pattern illustrating birth and life in Canada, typical for "babies," probably a big factor
IF IRCC requests additional documentation (odds are probably good the application will be routinely processed, no requests for such additional information or documentation).
Additionally, being a homemaker is well-recognized by IRCC as a common, typical situation. Parent staying at home with young children, in itself, should not be problematic.
What jumps out a bit in the scenario as described, however, is how the family is financially supported. Not that this is the focus of an inquiry into qualifications for citizenship, but it can be a collateral matter which invites some additional inquiry or even elevated scrutiny, depending on other factors. The explanation itself does not matter so much, so long as there is indeed a reasonable, credible explanation consistent with who the applicant and the applicant's spouse are, what their situation is. And again, this would come up only if IRCC requests additional information and documentation, and the odds are good that will not happen (but of course it might).