> Is it possible to embed/include the Firebird installer into my own
> custom installer?

Yes.

> So when the end user install my application, then the firebird service
> is automatic installed on his machine.
>
> Without the end user need to run a separate firebird installer.

Please check the InnoSetup script for details. If you have questions, please
ask them in Firebird-Support group, not in this one. Firebird-Java is
devoted to Java-related issues only.

Roman