Can I download photos from my husbands new iPad mini to my Mac? Do I just sync it?

Yep, just make sure to connect your iPad mini to your husband's Mac, open iTunes and navigate to your device settings. From the Photos tab make sure to select a location on his Mac where to sync the photos.

Finally click on sync. Be careful though, if your iPad Mini was never synced to your husband's iTunes, this will delete your multimedia contents form your iPad - make sure to tick "Manually manager music and videos" before you hit the Sync button.

How to Transfer Photos from an iPad to a Computer

http://www.wikihow.com/Transfer-Photos-from-an-iPad-to-a-Computer

Importing Personal Photos and videos from your iOS device to your computer.

http://support.apple.com/kb/HT4083

 Cheers, Tom 😉

iOS devices are designed to be synced with only one computer. Syncing with a second computer will remove items received by syncing with the first.

So if you have already synced your iPad with your computer do not attempt to sync with your husbands as this will remove stuff synced from your computer. To add your husbands photos copy them to your computer and then sync with your computer.