This is exactly what you think:
container.RegisterType<IEnterpriseClient<IInterface1>, EnterpriseClient<IInterface1>>( ... );
This is if you want only this closed, closed, generic account to be registered. For an open generic (and not just IInterface1) you can do:
container.RegisterType(typeof(IEnterpriseClient<>), typeof(EnterpriseClient<>), ... );
You mentioned that you tried this - what doesn't work?
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