You must file as married if you are married.
Here, however, your choice overrides his mother. If you file a joint return (married filing jointly), then your mother-in-law can't claim him as a dependent. It will take 6-9 months for the IRS to catch up, but eventually they will send her a bill for any part of her refund that came from claiming him as a dependent. If you file this way, you both answer "no" to the question, can someone else claim you as a dependent. Because your mother-in-law will most likely get a tax bill if you file jointly, you should consider the ramifications before you do this.
Your other option is to file your return as Married Filing Separately. That won't touch you mother-in-law. If your spouse has taxable income, he would also file as MFS, and he would answer "yes" to the question, can someone else claim you as a dependent.
This is a special set of circumstances that exist because he lived with his parent for more than half the year before getting married. Next year, his parent can't claim him as a dependent and you will just file MFJ.
