Graeme,
Others may disagree but if you want to remain with a file password solution, I would only protect the BE as the tables are the most important thing in any DB. I would convert the FE to MDE to secure it. Once you have done this you will probably have to re-create the link tables. Delete all LINK tables out of the FE then re-create the links (you should be prompted for the BE password). Using the linked table manager won't be any use as you need to re-create the links not refresh them.
Alternatively I would recommend using a workgroup security model rather than a database password. If you split a database into FE and BE (as in your case) the linked tables in the FE will adopt the same workgroup security rules as applied to the BE. This is also worth a look
10 tips for securing a Microsoft Access database | TechRepublic
I would however emphasise the importance of reading around the topic 'User level security' to ensure that your DB is completely secured. The use of a custom workgroup information file can be tricky. I would backup the FE/BE and system workgroup file just in case.
Hope this helps,
Dave