It is not a 'joint responsibility' to maintain licence validity, this responsibility lies with the licence holder alone.
Whilst there is a personal responsibility on the part of the licence holder to make sure they are valid I think there is a joint legal responsibility and this has been written into the Part A for both companies I've worked for no doubt sourced from EU-OPS:
EU-OPS 1.940
(a) An operator shall ensure that:
(3) All flight crew members hold an applicable and valid licence acceptable to the Authority and are suitably qualified
and competent to conduct the duties assigned to them;