How to make 2 differents networks to coexist

Hello, I have one nic pointed to
128.172.xxx.xxx for my intranet and the other one pointing to
200.44.xxx.xxx; I use the last one for internet and the first one for
my intranet; however, in order to browse my internal network, i have
to disable de 200.44.xxx.xxx; i'd like to know can they coexist
without having to disconnect one of them