Block time is what counts toward FAA flight/duty time restrictions so of course all block time during which you are on board the aircraft as a required crewmember should be logged, without regard to when or how much break time is taken. FAA also allows the PIC listed on the flight release to log all block time for the flight as PIC - take it up with the FAA if you don't like it. It's relevant since this was a US carrier operating on behalf of CX. Fact is (as we all know) if you're the captain, even on your break you are liable to be called up to the flight deck should a problem arise, I encourage my F/O's to do so even for minor questions. In reality it doesn't really matter unless you're applying for a new job. I wasn't even asked for my logbooks at my current employer; airlines will know what you've been doing based upon where you've been working, logbooks are a formality.