Once the customer’s card information has been collected (with the embedded or pop-up form options), it is passed on to Stripe’s servers where a corresponding temporary token is created.The temporary token cannot be reused for any other purpose.
Once the temporary token is created in Stripe, it will be passed to your (the merchant’s) website. With Chargebee in the picture, you would push this token and the customer’s personal information to Chargebee. Chargebee would then create a customer in your account and in Stripe.
Here's an image of the flow with the merchant website in blue, Chargebee in purple and Stripe in red:
Related Documentation
https://www.chargebee.com/tutorials/index.html