If his most recent pay stubs show his income would average out to be enough, then you would not need a co-sponsor. However, since it is so close, and he had not filed taxes, he may wish to go ahead and have all the documents ready from his mother just in case they would ask for a co-sponsor in your case.
Your dad would fill out the I-864, and your mom would fill out the I-864A. Their income would then be combined on your dad's I-864 to reach the 125% level for their household size plus your husband. Relationship to sponsor, #8 of the I-864A: mom checks c. and spouse. Part 2 #13 is filled out by your dad, your husband would be listed on line a, and he would sign and date it on #14. Part 3 is where your mom would fill in her info and sign and date it.
If your father or mother qualify on their own for their household count + your husband, then only one of them needs to fill out an I-864, even if they file taxes jointly. The I-864A is only used when a household member's income is needed to be combined with the one filling out the I-864 to reach the 125% mark.
