Oil is leaking into my coolant reserve tank, but water is not mixing with oil. What's the next move?

It's a 98 Honda Accord LX with 242,000 miles. I've been told it's a blown head gasket, but there's no water mist coming from the exhaust. Two weeks ago, a hose burst, and was changed. Two days later the mixture in the topped the radiator and the reserve tank and ran hot. Next day a shop replaced the radiator cap and I have been able to drive the car without overheating, but the mixture was still there. Recently the shop flushed the radiator, cleaned the reserve tank and applied engine/coolant sealant. The next day the mixture came backOil is leaking into my coolant reserve tank, but water is not mixing with oil. What's the next move?
If it's a automatic it could be a trans cooling tank inside the radiator failed, but I would have it checked by another shop. Head gasket failure doesn't always steam out the tail pipe! Stop leak in a cooling system can also look like oil depending on the brand.Oil is leaking into my coolant reserve tank, but water is not mixing with oil. What's the next move?
They may not have purged the air out of the system. There is usually one or two valves along your cooling system that allows you to get the air out of the lines. It looks like a nipple with a hex head. The mechanic may not of done his job correctly or fully and didn't purge the air out of the system. Try another shop and see what they say.
Cracked head or blown gasket. Coolant does not have to be leaking into a cylinder bore. There are oil and coolant passages through the gasket from the block to the head. Could be a leak between them.
Head gasket doesn't have to be blown, just a hairline crack in the gasket will push oil into your coolant. Go for a pressure test.