I am thinking of moving all our family photos from iPhoto into Lr, but my husband does not have Adobe software and still wants to be able to access our family photos.
Unless your husband uses the same computer as you do then it's not possible unless...
In LR you have the option when importing images into the cataloge of copying them, rather than moving them. Other words the images will remain in there original folder(s) in iPhoto, but will also show up in LR as copies. If he is using another computer, you can install LR on one more computer, see LR's EULA, for installation limits, usage etc. As for other family members consider a "cloud" option. Hope this helps.
Non-Lightroom users can access the edited photos via Exporting the photos to the hard disk; or via a Publish service (which is really just a different way of exporting photos). Or if your husband doesn't need to see your Lightroom edits, then no exporting is needed, he can view the photos as they exist on the hard disk.