You’re confusing what the life insurance does with what ownership of the house and wills do.
You can get mirror policies, or a joint life policy, which would pay out an amount sufficient to pay off the mortgage on the death of the first of you, with the policy paying the survivor. However, in the absence of wills leaving the house to the survivor, the survivor would get the money under the policy but not ownership of the house.
To achieve your aim, you need wills in which you each leave the house to the other. Or you could own the house as joint tenants, in which case what a will says would be irrelevant because joint tenancy mean the house can ONLY pass to the survivor entirely.
To achieve your partner’s aim, you’d need to own as tenants in common (as opposed to joint tenants) AND have wills. Then in his will he could give you a life interest in the house (meaning that after his death you could live in it for life), after which his share passes to his children (which should be in equal shares to any existing and future children you may have). You could also leave your share to whomever you wish, which may be to your one child entirely or to that child and any others you may have. This would mean (unless you have lots more kids) that once you’re both dead, his children will each have ended up with less than the child you’re about to have (an a further child if you want 2), since his share would be split minimum 4 ways and yours might go to only one child (who would also have received 25% of his share).
As you’re putting in the deposit, the deed of trust under which your respective shares in the house are recorded (if owning as tenants in common) should reflect the unequal initial contributions. So if you’re buying a £400k house with a £40k deposit and then sharing mortgage payments 50/50, your share should be 10% of the sale price plus 50% of the balance.
If you did not know all of the above already, you definitely need to take legal advice before committing to this very significant financial decision which will affect your and all the children’s futures.
It’s not unreasonable of him to want to ensure that his children inherit his share of the house, rather than any new partner you may get after he dies. You would want to ensure the same for your children.