Contrary to what you may think, this is not considered a good thing.
"The three dimensions of high EE shown are hostility, emotional over-involvement and critical comments" and it is measured formally through the Camberwell Family Interview, which uses verbal and non-verbal measurements. There are also other tests.If you appear hostile toward your (hostile) child, take too much responsibility (over-involvement) or too little (critical), you may be perceived as putting the patient at risk of relapse and poor prognosis.
Don't feel bad, though, the same judgment is made of parents of kids with other mental illnesses, and even of nurses.
For my part, I can tell you that my high EE, at times, was directly related to the attitude of the clinician and the current status of my daughter. When things were going well and we were all working well together: low EE. Perhaps EE is a measure of the clinician as much as of the family.