My young daughter and I watched this every night. It was a 4-5 part mini series shown in one of the major networks. It featured a mirror and characters like the White Rabbit, Snow White etc. Its premise was similar to the 10th Kingdom but this show was on earlier than 2000.
Is it possible that it was more than a miniseries?
Faerie Tale Theatre had 27 episodes over 6 years, and retold classic faerie tales with live action celebrites (Such as Vincent Price as the mirror in Snow White).
Faerie Tale Theatre on IMDB
List of Disney television films
Until we find out if this question was animated or not I would suggestion this.
I am still lost on the premise of the TV movie. With the description above it could also be Who Framed Roger Rabbit. White Rabbit and a cameo of Snow White since Disney would break up movies and air them in mini-series.