Did the husband abandoned his F-2 status when he applied for his H-1B status and my institution is no longer concerned with the husband's status?

As a school official, your better option is to direct your inquiry to USCIS regarding this student. But if the student involved has changed his status from F-1 to H-1B, then, he is no longer in F-1 from the date the change was effected by CIS. He is authorized to work legally in the US, but then only for the company that filed the H-1B petition for him. If this student was the principal of the F-1 visa, then, the F-2 visa for his spouse, his also terminated since the spouse' F-2 would also have been simultaneously changed from F-2 to H-4 dependent .

It really depends on what type of employer filed the H-1B visa petition on the husband's behalf. It is possible that it was a cap-exempt employer in which case he would not have needed to wait until October 1, 2013. You should only be concerned with the F-1 student that you have. Once the spouse has changed status to H-1B, that is no longer the concern of the school.

Unless the husband has been in H-1B status at some time during the past 6 years (in which case he would not be subject to the "Cap") you would be correct in assuming that he does not have work authorization until October 1, 2013 for a recently approved "Cap-subject" H-1B petition. If you are the Designated School Official (DSO) responsible for his record with SEVIS, you should request documentation from the F-1 student's husband and report the H-1B approval to SEVIS in regard to his maintenance of applicable F-2 dependent status. If your F-1 student is still actively enrolled and maintaining status then her spouse should still be entitled to F-2 status (albeit with a potential problem now of having worked without USCIS authorization under his recently approved H, assuming, again that he is not "cap-exempt" from a prior stint in H classification within the past six years). We recommend that you contact an experienced immigration attorney in this type of situation for guidance.