Am I entitled to have court appointed counsel to file a habeas petition, if I don't have money to pay an attorney?

Answer: There is generally no constitutional right to representation by counsel in a habeas corpus proceeding, but the court is empowered, within its discretion, to appoint counsel to assist a petitioner in preparing his petition. This is because a habeas corpus proceeding is civil in nature, and Sixth Amendment right to counsel afforded for criminal proceedings does not apply. 

However, appointment only happens when the interests of justice require it (if there's going to be a court hearing, for example) or when there is an unusual legal question at play. So, your husband can apply to be appointed counsel, or, if you get someone to look at his case and they find a novel legal issue or something they think would justify appointment of counsel then they can apply to be paid by the court to represent him. The factors generally considered are "the legal complexity of the case, the factual complexity of the case, and the petitioner's ability to investigate and present his claims, along with any other relevant factors." (29 F.3d 469). 

If your husband was not advised of the immigration consequences of his plea, then he may have a good issue, but not a very novel one, unfortunately. 

My advice is to consult with an attorney although of course I understand that can be expensive. 

Best of luck!