This is not income, in the same way that per diem paid to workers who are conducting work out of town is not income that can be used to qualify for a mortgage.
Does your husband claim deductions on the mileage?
If he did in fact claim the mileage income, and then the appropriate mileage and meals deductions, then I would say that yes, this is income.
But in your case, its just not income, unfortunately.
If it helps anything, I had some rather large deposits that were work expense reimbursements from my employer and were hitting my bank account during my FHA refinance back in the Fall of 2012. I had to write Letters of Explanation for these deposits, but they were not income by any stretch of the imagination. Some were for mileage, others were for hotels, planes, etc.
FICO 9: 
Filed Chapter 13 on 6/1/2017 after job loss. Discharged 6/1/2022.
Goal: Gardening!
Filed Chapter 13 on 6/1/2017 after job loss. Discharged 6/1/2022.
Goal: Gardening!
It is not income, it is reimbursement for the gas used to travel for work. You paid for the gas already so you are just being reimbursed the cost. If the deposit is fairly large, you may have to source it. But it isn't income. It's your income being paid back to you.
Cards: Orchard Bank ($1100) | Cap1 Cash Rewards ($2500) | Chase Freedom ($1000) | Best Buy ($2500) | Discover It ($1000) | Barclay Rewards ($2500) | Current scores: EX FAKO: 684, CK TU: 649, FICO EQ: 680, FICO TU: 698, FICO EX: 658 Happy Homeowner Since 2/6/13! 
Last App: 4/5/13 Gardening until July 2014