Texture in musical theatre can often be described as melody and accompaniment. Because it is especially important for the lyrics to be communicated clearly to the audience, this kind of texture enables this to happen with the orchestra providing support.
There are lots of exceptions to this however!
Fugue for Tinhorns from the musical, "Guys and Dolls" begins with a melody and accompaniment texture at 0'13, showing a man with a newspaper talking about the horse he's betting on. At 0'32 the first man keeps singing "can do" as the second character comes in with the first melody, creating a polyphonic texture. When the third singer comes in there are 3 simultaneous melodies heard creating quite a comedic effect that helps portray the enthusiasm each character is feeling.
The Lion King is perhaps the only famous musical to start with a monophonic texture with the iconic acapella melody sung by Rafiki. The texture becomes very conversational with lots of melodic exchanges and parallel harmonies which helps conjure up the excitement of the musical's setting at the beginning of the show.
The texture of Defying Gravity can be described as melody and accompaniment or homophonic for the vast majority of the song with one melody being sung with the rest of the texture providing backing.
The use of ostinati and short melodic snippets discussed in the page on melody only take on supportive roles so it wouldn't be accurate to define the texture as anything other than melody and accompaniment in these sections too. However, there are some exceptions to this:
When the two characters sing together it is usually in unison, for example from bar 15 (0'23). When they sing the chorus together from bar 103 (3'29) it is also mostly in unison though there is some close harmony in parallel motion to keep the music varied and interesting. At 4'10 there is also some 2-part harmony in parallel 3rds which helps to show that the characters are in agreement and have a sense of understanding for one another.
The final section of the coda is the only place where the vocals are polyphonic with Elphaba singing above the ensemble's exclamation of "No One Mourns the Wicked" (bar 168, 5'30). This texture clearly shows that the characters are clashing and makes the finale of the act extremely dramatic and suspenseful. On the phrase "got to bring her down", the chordal melodies are arranged for the voices and orchestra in contrary motion which makes it expansive and all-embracing.