Propagating terminal settings

Hi all,
I have a question about terminal settings.

I am using ssh (OpenSSH_4.7p1-hpn12v18, OpenSSL 0.9.8f)

On my own linux PC the terminal erase character is Ctrl-?.

I am using ssh to log into another linux PC where the erase character is
set to Ctrl-H.

Backspace works fine when I am logeed in locally on the second machine
but when I am logged in with ssh from the first machine it produces ^?
instead of erasing in many programs (vim for example).

I can fix this by doing stty erase ^? to change the setting after I log
in but it is impractical to do this every time. Is it possible to get
ssh to propagate the terminal settings from the terminal it is run in to
the one started on the remote machine?