Regulation 5(h) of the IIP regulations states that "the applicant and, or any of his dependants shall not be an individual who at anytime was found guilty [...] for any criminal offense, other than an involuntary offense, punishable with more than one year imprisonment." Furthermore, Regulation 6 states that an applicant (which by definition includes a dependent) who has a criminal record "shall not be approved for citizenship under the program, unless Identity Malta is satisfied that the applicant is still worthy of being considered for approval due to special circumstances to be demonstrated by the applicant." Therefore, two criteria seem to apply whereby, if the crime committed by your husband was punishable with more than one year of impirsonment, he is automatically not eligible to apply; and if the crime was not punishable with such term, he would need to demonstrate to Identity Malta that he is worthy of eligibility, with time and the fact that he has since started a family presumably being in his favor.
