If you are sharing the same iCloud account any data you sync with the account (such as contacts) is merged, and any actions you take on one device (such as deleting contacts) also takes place on the device(s) sharing the account. To fix this, you need to be on separate iCloud accounts.
One of you needs to migrate their iCloud data to a separate iCloud account/ID. In your situation, this might be able to do with his phone. To do this, go to Settings>iCloud on his phone, tap Delete Account, choose Keep on My iPhone when prompted. Then sign back in with a separate ID and choose Merge to upload the data to the new account.
Once you are on separate accounts, you can sign into each account separately on icloud.com and delete the other person's data from each account.
To get the contacts on you iPad into your husband's iPhone and iCloud account, make sure his phone has Contacts turned to On in Settings>iCloud. Download the app My Contacts Backup on your iPad and use this to back up your contacts as an attachment to an email. Send this email to your husband. Have him open it on his phone and tap the attachment to import the contacts to his phone, and to his iCloud account.
You are both using the same iCloud/Apple ID. Therefore whenever someone makes a change on a device, it is pushed to ALL devices using the same ID. So, in order to avoid this in the future, you should each get your own iCloud/AppleIDs.
The only thing I can say about the iPad still having your contacts is that Contact synching was NOT turned on in iCloud, or it is not signed in to iCloud, or both.
Thank you randers4! I entered here searching for the same problem as philly gal and read your instructions on how to fix the situation and followed your advice, I downloaded My Contacts Backup app, very simple steps to follow with this app and I sucessfully transfered my contacts to my husband iphone. Your wise advice helped us a lot. Thanks again!