"When I used to read fairy tales, I fancied that kind of thing never happened, and now here I am in the middle of one!"

The 1945 musical Anchors Aweigh is famed for its dance sequence that merged live action with animation. Wikipedia:

The movie is remembered for the musical number in which Gene Kelly dances seamlessly with the animated Jerry Mouse (voiced by Sara Berner). Tom Cat appears briefly as a butler in the sequence supervised by William Hanna and Joseph Barbera. The animation was entirely undertaken by Kenneth Muse, Ray Patterson and Ed Barge.

Originally, the producers wanted to use Mickey Mouse for this segment. Some sources claim Walt Disney initially agreed to loan out Mickey, but Roy Disney rejected the deal. According to Bob Thomas's book on Roy Disney, the studio was in debt after World War II and they were focusing on trying to release their own films out on time. According to Roy, they had no business making cartoons for other people. After Disney turned the offer down, Kelly went to Fred Quimby, the head of MGM's cartoon studio. Quimby was also not interested, but Kelly persisted, reportedly showing up at Hanna and Barbera's office to press the case. The dance sequence required meticulous storyboarding; after Kelly's dance was filmed, the animators used rotoscoping to painstakingly match the animated character's movement to Kelly's, even down to their shadows cast on the polished dance floor.

Gene Kelly's first choice as a dance partner was Mickey Mouse. Not only was Mickey the most famous cartoon character in the world, but Walt Disney had the expertise Gene Kelly was looking for: Walt was the first to mix live action and animation 20 years previously in the Alice Comedies.

Alice’s Wonderland—the last film Walt Disney made in Kansas City, Missouri—depicts the animated adventures of a true-to-life young girl in a make-believe world.

In the original 1923 short film, Alice arrives by train in “Cartoonland.” A large welcoming committee of animated animal characters greets her with excitement and adoration....Roy Disney was taught to hand-crank the movie camera...Walt directed the live-action and single-handedly created the animated drawings.

The Walt Disney Museum devotes an entire room to the Alice Comedies, which consist of 57 short films produced from 1923 to 1927. Walt tired of the effort required of this format and devoted himself to synchronizing sound in 100%-animated pictures. Steamboat Willie, which introduced Mickey and Minnie Mouse, was released in 1928.

Below--part of the Alice Comedies display in the museum: