Does the new immigration law affect my husband?

President Obama did not sign a new law recently. The policy statement may or may not result in some temporary relief for your husband. I suggest you meet with an immigration lawyer to discuss his options.

Unfortunately there is no "Obama new law". So far it is just talk and hope. If your husband was deported in absentia, then he might have to wait in Honduras for 5 years before he can come back on your petition.

There is no new immigration "law," rather there is a new direction for the enforcement part of immigration, called ICE (Immigration and Customs Enforcement). The new emphasis will be on removing (deporting) those removable aliens who have committed crimes or pose a danger to the United States. That certainly does not sound like your husband. All other removals will be placed "on a back burner" for now and dealt with in the future. I do not know what steps you have taken so far to sponsor your husband but I assume that you have filed a I-130 petition based on your marriage? If you did and it was approved, it would also count towards making your husband a lesser priority for removal. In any event, unfortunately he would still need to go out of the country and try to get a waiver (not a pardon as you stated) because he entered illegally. That waiver (known as a 601 Waiver) needs to be well prepared and presented on the basis of extreme hardship to yourself as his U.S. Citizens spouse. Now listen carefully: the hardship to your children (even the one with seizures) does not count directly because the waiver is based only on hardship to spouses and parents, but to the extent that the hardship to the children affects you as his spouse, it is an important part of what needs to be presented and argued in support of the 601 Waiver. Also, depending on the facts, your husband's removal order because he did not go to the hearing may be able to be set aside (vacated) and his case reinstated. This is a matter that depends on too many factors to address here, but generally if he knew about the court date and just did not show up, there would not be good reason to try to rescind the removal order and reopen the case. If the case could be reopened, he might be eligible for various relief. I hope this helps and wish you the best of luck.

He may be able to apply for deferred action and be placed under an order of supervision allowing him to obtain a work authorization based on the premises of the recently announced policy.

It is unclear as to the extent of the new policy, but it does not sound like the type of case that would qualify. You should continue to monitor the law as it progresses.