Who issued the ticket? They and their computers should have known whether the code-share was legal or not. If you look up the MH codeshare flight number on EF or a similar tool and look at the rules it should clearly state that. (Not that knowing that the ticketing carrier screwed up is going to do much good in this case, although if they did and left you in a tight spot they should do whatever it takes to solve your/their problem.)

And what does the poster mean who says 'that's what code shares are for'? I was pretty sure that code shares were a marketing tool that a carrier could use however they saw fit, including perhaps an unmarried segment between two cities.

More generally re flight-watching: these days there are more inexperienced airline agents, more complicated rules, computers talking to other airlines' computers using disparate data bases and perhaps buggy code, and bankrupt airlines with no room in the budget to care much more about their pax than legally required. It is alas prudent to keep watch on all your forward bookings lest you receive surprising news at OLCI or the airport desk.

The ticket number is the golden one, although PNRs (cross-referenced to the operating carrier when necessary) are usually handy. A copy of the rules for your flights can also be handy in the case an agent is dead wrong - quoting the text will often let reason reign.