Well, yes and no. Obviously your husband cannot take maternity leave; he's not the one having the baby.
A prospective father CAN take FMLA in some situations. FMLA eligibility is set by Federal law. In order to take FMLA, ALL of the following must be true:
1.) The employer must have 50 employees or more within 75 miles of the employee's location
2.) The employee must have worked for the employer for no less than 12 months
3.) The employee must have worked a minimum of 1,250 hours in the 12 months immediately preceding the leave
If ALL THREE criteria are not met, FMLA does not apply.
Assuming that the criteria is met, there are still a few other things to consider:
FMLA would be available before the birth ONLY if he was needed for your care. If you are capable of self-care, he is not eligible for FMLA prior to your giving birth. The employer IS entitled to medical documentation that his presence is necessary for your medical well-being.
After birth, he is entitled to up to 12 weeks of UNPAID leave. His employer CAN require that he use his vacation during that time and CAN insist on up to 30 days notice of his intent to be out. (Give or take a couple of days either way since we all understand that babies can't read calendars.) However, if he plans to take that time intermittantly (maybe because he can't afford to be out that long without pay) that is the ONE AND ONLY TIME that an employer can refuse to allow the time. Intermittant baby-bonding leave can only be taken at the agreement of both employer and employee.
When it comes to his initally going out, he CAN be required to adhere to regular company call-in procedures or follow the protocal for leaving work. He doesn't get to just walk off the job or just not show up and claim, Oh, it's FMLA, you have to excuse me from following policy. They don't.