I'd just like to point out here that it is usually technically possible to interline bags from airline A onto airline B, where A and B can be pretty much any of the airlines out there in operation today, but the right to have your bags interlined only arises when you are travelling on a single ticket that involves a connection between these airlines.
It is increasingly the case that airlines REFUSE to interline bags across separate tickets; some will require that the airlines are in the same alliance; some might require there to be a minimum amount of time at the transfer point; and some refuse point-blank.
An airline that checks a bag through onto a second ticket is assuming liability in the case that the bag should be missing or delayed; this is an onerous liability which most airlines will NOT want to assume when there is no requirement for them to do so.
If Etihad, as so many people have said, are happy to check bags through to different airlines on different tickets, I would not take that as confirmation that this is stated company policy. It could be - and it could just as easily be changed with no notice (like so many other things about the EY experience of late). Or it could just be down to ignorant/unwitting check-in staff who are less likely to refuse a request from a status passenger, for instance.
To the OP: there is probably a reason why you are travelling on separate tickets - it may not have been possible to buy your desired travel on one ticket, or it may have been far more expensive. However, when you decide to travel on separate tickets, you are assuming added risks. You must allow sufficient time between tickets for all eventualities - if your inbound flight is delayed, then you will not be rebooked or carried for free on a later flight to your final destination, because you will have missed your flight on your second, unrelated ticket, and the first airline will have no responsibility to making this up to you.
You must always plan pesimistically when travelling on separate tickets. Assume that your flights will be delayed. Assume that your bags will not be interlined. Assume that you will face long queues at immigration, customs, and check-in for your next flight.
And good luck with your travels!
FINALLY - when you do have a bag interlined across separate tickets, BE SURE TO KEEP THE LUGGAGE RECEIPT, AND MAKE SURE YOU ENQUIRE WITH A STAFF MEMBER OF THE NEXT AIRLINE (and any subsequent "new" airlines) BEFORE BOARDING THE FIRST FLIGHT OF YOUR SECOND TICKET TO ALERT THEM THAT YOU HAVE A BAG IN TRANSIT. The "second" airline won't have been expecting that you have bags in transit - after all, as far as they know, you are actually only starting your day's travel with them - and in many cases, the bag may not be loaded unless you alert them to its existence, despite it being labelled for their flight and handed over to them at the interconnection point.