You could snag your audio off with "goldwave" (free to try), audio editer (or other audio editer). Mix it in there very nicely using copy, paste, mix methods.
Drag and drop a video onto the Audio editer window. The audio should be in a normal codec that exists on the computer, then the audio editor will open just the audio. If the audio is in some form that it doesn't understand that makes things harder. It will have "de-muxed" the audio off of the video.
Open, or drag and drop in the Music that you would like to add to this sound track. Now you have 2 Wav files that you can see visually, The Original audio and the music.
Select the window for the music track without poking around in the wave there, and select EDIT COPY. Now select the window that has the videos audio in it, and select EDIT MIX, selected the quantity of the mix, and preview it , then Ok it to get the mix. Keep your music lower than your first guess, if you expect anyone to be able to hear the audio of the original video.
Of course you can do about anything before or after or during, like poke selecting where you want the mix to land. Making fade-in and fade-out for either of the waves. Just try and keep the TIME straight, dont clip off the front of the video audio, dont paste into the front. Liberally apply the undo :-) (with the free version you run out of actions, and the session is ended &#^$&)
Once you have finalised the mix Save that out as a Wave file (or mp3) in 16bit signed stereo. make sure you put this sound mix somewhere you know where it is.
Now fire up Virtual Dub, or any program that can re-mux this audio track back on the video. In virtual dub, Drag and drop your video onto the virtual dub windows. In the VIDEO menu Select DIRECT STREAM COPY , in the AUDIO menu select AUDIO FROM OTHER FILE , it will then want you to put in an audio file, the one that you just edited. The audio that you put in will be replacing fully the original audio.
Select FILE, SAVE AS AVI.
Of course anything that can go wrong will, you must have codecs, this process doesnt even work with some of the more complex codecs.
There are many many video programs that can be used to do audio mixing, on a timeline, and output the mixed audio, most of them can be set so the video is not recompressed (unchanged). some of them free, most of the good ones very expencive and complex. This is just one quick way to do it.