I just wanted to thank all the ladies who weighed in and voted. After a lot of thought and discussion with DH, I'm going to apply using my married name. The HR woman will know who I am, because DH double-checked that my application wouldn't pose a conflict, but he's not going "schmooze".
We let the deciding factor be that I'm genuinely interested in the job and the company, not to mention very qualified for the position. If the job hadn't been in his office, I would have applied already. He told me to just take him out of the equation, and once I did, it was an easy answer.
(BTW, for anyone who was interested, he didn't mention the job in the first place because it is pretty entry level - not to mention a big pay cut. But hey - not as big a pay cut as being unemployed.
Also, there are no internal obstacles to applying; as I mentioned in my OP, it is not uncommon in our fields for husbands and wives to work together and the company already has several couples ((both married and living together)) employed there. While DH's is a senior position, there would be no situation in which I would report to him. But thank you to those who offered up thoughts that working together might not be a good idea; I know for some it might not be and I think you all raised good points. I promise if I get the job and it's a terrible, awful, no good, very bad thing, I'll post in TIP and mention that you all warned me ahead of time.)