A "Dual Media Discharge" refers to a maintenance item that is performed usually once every ~10 years. It involves a lot of training, preparation, setup, and planning (the actual maintenance doesn't take very long, assuming everything goes according to plan). They replace some very highly radioactive portions of the ship's propulsion system, making it a noteworthy accomplishment.
These guys here are joking about your husband and what he might do after spending a little too much time out drinking on liberty. (The "dual media discharge" probably refers to the combination of vomiting and urinating that usually follows excessive drinking)
As far as the acronyms are concerned, here's a quick list:
PBO: Not sure what this is. He probably meant to say "PVO" which stands for "Primary Valve Operator", which is a qualification necessary to operate any valves on the primary reactor coolant system.
3M301: The "3M" stands for "Maintenance Material Management", which is the program that the Navy uses for handling all of its scheduled maintenance. The "301" refers to a particular qualification, in this case "Maintenance Worker", which is necessary to perform maintenance using the 3M system.
QA301: The "QA" stands for "Quality Assurance" and it's another program that the navy uses to ensure that work done on certain vital areas are done correctly, using lots of paperwork, oversight, and careful controls. The "301" also refers to being a maintenance worker, but within the QA program.
SIR: This stands for "Senior-in-Rate" which refers to the highest qualification he can receive without being a supervisor. For MM's it is (at least on a submarine) Engineroom Supervisor. Don't be confused by the title. It's Senior-in-Rate, not a supervisory position.
The various other quals (302, 303, etc) refer to progressively higher and higher levels of qualification. I believe 302 is RPPO (Repair Parts Petty Officer) and 303 is Work Center Supervisor.