  Manifolds endowed with three foliations pairwise transversal are known as
3-webs. Equivalently, they can be algebraically defined as biparacomplex or
complex product manifolds, i.e., manifolds endowed with three tensor fields of
type $(1,1)$, $F$, $P$ and $J=F \circ P$, where the two first are product and
the third one is complex, and they mutually anti-commute. In this case, it is
well known that there exists a unique torsion-free connection parallelizing the
structure. In the present paper, we study connections attached to
non-integrable almost biparacomplex manifolds.
