Aryanna Hering didn’t have pay stubs or tax forms to document her income when she shopped around for a mortgage last year—a problem that made it tough for her to get a loan.

But the nursing student who works part time providing home care for children and the elderly eventually hit pay dirt: For a roughly $610,000 home loan, a mortgage company let her verify her earnings with 12 months of bank statements and letters from clients. Ms. Hering said money she collects from roommates and from renting to Airbnb guests covers more...