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There were not many military interventions by the USSR in the decades between WWII and ISIS. The Soviet Union only fought with Afghanistan and China during these decades, and a couple of 'invasions' of Warsaw pact countries. This list shows where the USSR fought in these years.
Comparatively, the US actively fought in Vietnam, Korea, Laos, Cambodia, Philippines, Nicaragua, Panama, Libya, Iraq/Kuwait, Cuba, Guatemala, Chile, Honduras, El Salvador, Somalia, Afghanistan, and more during these same years.
The comment above about supporting Iraq against Iran in a proxy war is the closest there is for this time period.
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I can't think of a single one militarily. The last time I can think of any actual cooperation was under "Nunn/Lugar" which involved the deconstruction of the former Soviet Union's vast stockpiles of nuclear weapons.
There are rumors that the USA and Russia are cooperating in Syria...but Russia's stated goal is to keep Assad in power whereas the USA has said it's goal is to have him deposed.
Turkey is also a member of NATO whereas Russia most certainly is not.
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Depends somewhat on your definition of 'engagement' and 'conflict'. (Or, in the case of Syria, your definition of 'joint'...)
The UNTSO peacekeeping/observation mission in the Middle East had a permanent allocation of both American and Soviet military representatives (36 of each) between 1973 and the end of the Cold War. UNTSO still has Russian representatives. Not quite a combat role, but definitely in a combat zone. This was, I believe, the first time the USSR ever contributed personnel to a UN peacekeeping mission.
After the end of the Cold War, Russia began to take a more active role in UN peacekeeping operations. Russian troops were deployed in at least four of the Yugoslav peacekeeping operations, all of which also had US participation: