If you're looking for a mortgage to buy a home for yourselves, then no. Irish law grants your husband certain legal rights in respect of a family home, regardless of whether or not he's named on the property or mortgage, so lenders will insist that he's on the mortgage.
For self-employed people, lenders take an average of 2 or 3 years' income into account, so even if his income is up and down, it might still count for something on average. Have a chat with a mortgage broker.