One way would be to plug the analogue (phono) audio outputs of the DVD player into a small audio mixer (the type you can get from Maplins etc). You then plug the mic into the mixer and then the output of the mixer into your amplifier. You would need to adjust the relative levels of the DVD and mic, and the master output level using the mixer.
I have done this with a small Behringer mixer using a Shure mic with excellent results. My mixer also has AUX sends so you can process either signal via an effects unit if you want to add reverb, echo etc
Jez