Dear Keren,

> adukkhamasukhaa upekkhaasatipaarisuddhim catuttha.m jhaanaaa
> upasampajja viharati.
>
> In this sentence there are both adukkhamasukhaa which is vedanaa and
> upekkhaa. What exactly is this feeling of neither-painful-nor-
> pleasant?

Well, it is not an indifference of ignorance.
It's a kind of peaceful equipoise. Seeing with wisdom the ups and downs
of mind, feelings of pleasure and pain, one lets them go, and turns to
serene observation, as in:

"He discerns that 'This agreeable thing has arisen in me, this
disagreeable thing... this agreeable & disagreeable thing has arisen in
me. And that is compounded, gross, dependently co-arisen. But this is
peaceful, this is exquisite, i.e., 'upekkhaa'."

http://www.accesstoinsight.org/canon/majjhima/mn152.html
http://www.lioncity.net/buddhism/index.php?showtopic=22344

Metta,
Dmytro