A minor under the age of 18 cannot own land or property in the UK. His share would have to be owned in trust by trustees (who could be you and your OH) for his “beneficial ownership”. However, before you worry about whether it’s possible you need to think about whether it’s desirable.
There are many scenarios but here’s just one. If you or your OH dies the survivor (as a tenant-in-common) will own one third of the house. Your son will own one third and the deceased’s third will either be bequeathed as part of the deceased’s will or (if no will exists) will be distributed under the intestate rules. If your son acquires this third through either of those methods and thus will own two-thirds of the house the surviving partner, with a one third share, will be in a very vulnerable position.
You have not explained your circumstances but you mention “my” son, giving an indication that he is not the product of your current partnership. If your OH is not his true parent and you die first, your OH will find him/herself with a third share in a house where the other two thirds are owned by a person who is not his/her son. I know this all sounds very pessimistic but dreadful family fall-outs often ensue from such situations (even though the arrangements are made with the best of intentions when everything is hunky-dory).
You should not embark on this without taking legal advice. At the very least you should have an agreement drawn so that in the event of the death of one of the three of you the survivors can remain in the house should they choose to do so. It sounds a bit clinical and hopefully it is unnecessarily so, but awful situations develop years later for the want of a bit of thought at the state you are now at.