Is it possible to integrate AWS Codepipeline and Jenkins in such a way?
As now CodePipeline has direct Bitbucket cloud support [1] and also supports the jenkins as custom stage directly [2] you can setup the CodePipeline which will use the bitbucket as source stage and jenkins actions as part of stage so that we can still use the jenkins for all the testing and once there is success from the jenkis we can go ahead and do the Deployment to CloudFormation.
[2]https://docs.aws.amazon.com/codepipeline/latest/userguide/tutorials-four-stage-pipeline.html