I work in a library and a few years back the librarian went job share. She was in charge of 4 libraries and about 2 dozen staff at the time. We were all a bit dubious as to how it would work but it actually went fantastically well. The woman who got the other half of the job was really nice and great at her job and they would get together once a week and catch each other up on what was going on, work plans etc. They also balanced each other out really well and since they were working together they were both pretty chilled out - it took a lot of pressure off the original boss since she had someone to share the load and exchange ideas with. Unfortunately, due to restructuring within the council they were transferred to the main branch after a couple of years, but they still work together and as far as I know it still works really well for them, so it can be done. I'm also not sure of the legality of not allowing you to do it, I'd check that if I were you.