How to measure Golang integration test coverage?

I am trying to use go test -cover to measure the test coverage of a service I am building. It is a REST API and I am testing it by spinning it up, making test HTTP requests and reviewing the HTTP responses. These tests are not part of the packages of the services and go tool cover returns 0% test coverage. Is there a way to get the actual test coverage? I would expect a best-case scenario test on a given endpoint to cover at least 30-50% of the code for specific endpoint handler, and by adding more tests for common error to improve this further.