While making an adventure map I noticed that you can punch paintings in adventure mode. The only workaround I know is by making them invulnerable.
Related issues
Comments

To prevent it from being breakable, you can give the painting the invulnerable NBT tag using /data. Keep in mind that this also prevents you from breaking it in survival mode.
Thank you for your report!
We're tracking this issue in MC-579, so this ticket is being resolved and linked as a duplicate.
That ticket has already been resolved as working as intended, which means this is not considered a bug and won't be fixed. Please do not leave a comment on the linked ticket.
If you haven't already, you might like to make use of the search feature to see if the issue has already been mentioned.
Quick Links:
π Bug Tracker Guidelines β π¬ Community Support β π§ Mojang Support
π Project Summary β βοΈ Feedback and Suggestions β π Game Wiki
This appears to be a duplicate of MC-579,Β which was later resolved as Works As Intended. This "issue" you are experiencing is working how it was intended to function. See the parent ticket for more details.