The closest you can do is give the other person full permissions with the house. You can manage your permissions from the housing menu I think. They still won't get a free telleport, and they can't use the mailbox. But they can enter, access chests, and decorate if you so allow.
I have a character in a similar circumstance, but that's as good as you can get.
Hi, my name is:
...and I'm an Alt'aholic.
1 - The house is shared between all your characters.
2 - In the house management, you can give access rights to a specific character and to your kinship members, from none to full access.
3 - As mentioned, other persons will not be able to teleport to your house, they will have to get there by normal travel.
Even the smallest person can change the course of the future!
One idea you could try is to get 2 houses, one for you and one for your friend, in the same housing neighbourhood. The closer together the better. Although you can't travel direct to the other player's house, you can still visit eachother really easily using your own house travel skill. Then like others have said, you can set up the housing permissions to give eachother access.