If my husband got arrested, can he get some type of work permit with a DWI on record?

Generally, a single DWI arrest or conviction will not stand in the way of eligibility for immigration benefits. Significantly more information is needed, however, to determine potential eligibilities for your husband to qualify for a visa or status that includes authorization to be employed. There really is no substitute for you and your husband to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options, and strategies to attain your goals, and who then could offer legal representation in the often complex application process.