If I'm married to an illegal who was deported and we have 3 children together, how can I bring him back to the US?

Once he has satisfied the conditions of his deportation order (he may be barred from reentry to the US for a period of 10 years), you can petition for him to reenter with a valid visa.  If he is eligible to enter before that, he may need  a waiver, if he can prove the necessary grounds to qualify for the waiver.