Yes, it is certainly possible to do this. In fact, you're not the first author to do so although from the sounds of things you may be mixing it up a lot more than previous attempts have done.
The most famous example is probably James Joyce's Ulysses which adopts wildly different narrative techniques between chapters. One of them, chapter 15, is written entirely as a stage play, complete with directions.
(Stephen, flourishing the ashplant in his left hand, chants with joy the introit for paschal time. Lynch, his jockeycap low on his brow, attends him, a sneer of discontent wrinkling his face.)
STEPHEN: Vidi aquam egredientem de templo a latere dextro. Alleluia.
(The famished snaggletusks of an elderly bawd protrude from a doorway.)
THE BAWD: (Her voice whispering huskily.) Sst! Come here till I tell you. Maidenhead inside. Sst!
STEPHEN: (Altius aliquantulum.) Et omnes ad quos pervenit aqua ista.
THE BAWD: (Spits in their trail her jet of venom.) Trinity medicals. Fallopian tube. All prick and no pence.
And so on. Some of it is written in rather more accessible language than the above sample from the beginning of the chapter. In fact, a play based on the chapter, Ulysses in Night-town, was performed on broadway in the 1970s.
You may also be interested in chapter 17 which takes the form of a series of questions and answers, since stylistically this bears a vague similarly to the dialogue prompts of a play:
What act did Bloom make on their arrival at their destination?
At the housesteps of the 4th of the equidifferent uneven numbers, number 7 Eccles street, he inserted his hand mechanically into the back pocket of his trousers to obtain his latchkey.
There are also snippets of stage directions and other theatrical paraphernalia, in a rather more limited form, in another famously difficult novel, Thomas Pynchon's Gravity's Rainbow.
—(Quietly) It’s been a prevalent notion
So the short answer is: yes, it is possible to mix narration styles within the same work. Ulysses is one of the most famous and lauded books in English literature partly because it makes such varied use of narrative styles.
However, you do need to be aware of what you're doing and who you're aiming your writing at. Joyce was making a self-conscious decision to push the boundaries of what a writer could do with the form of the novel and the results are often quite impenetrable to the casual reader. It's not a book you can just pick up and appreciate for its exciting narrative flow.
He also adopted these various forms for good reason. He used the play format because he wanted, in this chapter, to produce a hallucinatory effect in which reality and his character's internal imaginings blend into nightmarish scenes. He felt, given the more realistic approach taken in the rest of the novel, that simply writing it as a narrative would be too jarring.
If you switch between a free-flowing narrative and theatrical lines inside the same text, you'll be forcing the reader to stop and re-examine what you've written. This kind of coming up short can be a very powerful technique to signpost the reader at areas of the text you want them to consider more carefully. If you use it throughout a work, they'll likely do this at first, then eventually get used to it.