basic BIND / sendmail question

[mbh]

Hello everyone ... newb here.

Just a quick question though.  I have taken over the position of
network admin for an ISP.  We have two DNS servers, both running BIND
9.2.1 and a mail server running sendmail v8 (sorry, that's all I could
find).  I realize that what I'm asking involves knowing quite a bit
more than I presently know, so, I am asking only if something is
possible.

I have a potential customer who will switch to my service if I can host
his domain 'gigerich.com' (or something like that) as well as allow
them to maintain their email addys of  'whoever at gigerich.com'

My domain name is NOT that at all.  SO ... can I make my BIND and
sendmail recognize the new domain (without breaking mine) as well as
get and forward all their mail?

That's all for now.  :-)

I can see easily how to add a host to my DNS records as in
'newhost.mydomain.com' with an associated IP, but that's not what I'm
asking.  Well, I'm pretty sure that's not what I'm asking.

Thanks to anyone who can help.
Michael