Currently, the CDI specification doesn't define, when is the around-invoke method of a target class called, with regard to CDI interceptors.

The spec. only says, in 9.4, towards the end:

Interceptors declared using @Interceptors or in ejb-jar.xml are called before interceptors declared using interceptor bindings.

Currently, the order happens to be (in EAP6):

1. @Interceptors and ejb-jar.xml
2. Around-invoke method
3. CDI interceptors

In the following example the order of interception would be:

1. FirstInterceptor
2. SomeClass.aroundInvoke
3. ThirdInterceptor
   
   

   public class SomeClass {
     @ThirdInterceptorBinding // bound to ThirdInterceptor
     @Interceptors(FirstInterceptor.class)
     public int doSomething() {
       // ...
     }
   
     @AroundInvoke // comes second
     public Object aroundInvoke(InvocationContext invocationContext) throws Exception {
       return invocationContext.proceed();
     }
   }
   

This problem manifests in this (currently skipped) test:
https://github.com/weld/core/blob/1.1/tests-arquillian/src/test/java/org/jboss/weld/tests/interceptors/retry/RetryInterceptorTest.java