Can I upload a Time Machine backup (Passport) made on my computer to my husband's computer?

I'm afraid that my present Macbook is starting to have problems. I have an old Time Machine backup that I made on a Passport USB drive last year (using OS 10.6) so I can transfer the contents of my computer to my husband's Macbook (also OS 10.6). But when I connected the Passport, I got a message saying, "This backup was created on a different computer. If you reuse this backup it can no longer be used by the original computer."

I'm not sure what the implications of this are. I'm pretty sure I created the backup on my computer, but it might have been made on my husband's computer. In any case, I'd like to make a new one on my computer and upload it to my husband's as planned. Question:

1. Is there a way I can check to see which computer the backup was made on?

2. If it's an old backup of what's on my computer, is there a way I can update it, rather than go through the long process of creating a new backup? (The USB drive is 1 TB, so an original backup takes forever!)

3. If it's a backup of what's on my husband's computer, can I overwrite it ("Reuse Backup"?) and then upload it to his computer?

Thanks for any information out there!