I would check to verify the end user wants the fabrication to be in accordance with MIL-STD-278, as mentioned it has been replaced with the Tech Pub 278 for most new builds. A lot of people still refer to the Mil-Std when in fact they mean NAVSEA TECH PUB S9074-AR-GIB-010/278.
That being said, there are instances where the old Mil-Std is still the fabrication document required, but that introduces other complexities into the equation. The use of the old Mil-Std-278 requires the use of many older military standards for filler metals, some of which electrode manufacturers have stop producing (now you have to ask for deviations/exceptions and get the substitute filler metals approved), base metals that may or may not be readily available, inspection and NDT techniques and acceptance criteria to the old NAVSEA inspection standards, etc.
You will have to qualify your welding procedure and welders to the old Mil-Std-248. You will have to verify which revision they are requesting, because if it was the latest revision, you will have to have a training program for the welders approved before they can be qualified to actually weld anything. There are consultants that can guide you through the process.
The point I am trying to make is that it is not a case of simply using commercial grade base metals and filler metals, qualifying the welders and striking an arc. It is much more involved and it can take the unwary by surprise.
I have several clients that weld for several of the shipyards and it is no easy task to get your paperwork in order before starting the actual fabrication. It can take several months to get your procedures qualified, documented, and approved by the shipyard before fabrication starts. Don't start fabrication without the proper approvals in place or you stand the risk of scraping everything. Even the inspections, which are mandatory at various stages of fabrication, must be performed by individuals qualified and certified in accordance with the proper military standards or the work will not be accepted by the end customer.
Drop me a private message if you need help. I can steer you in the right direction.
Best regards - Al