  For a smooth, projective complex variety, we introduce several mixed Hodge
structures associated to higher algebraic cycles. Most notably, we introduce a
mixed Hodge structure for a pair of higher cycles which are in the refined
normalized complex and intersect properly. In a special case, this mixed Hodge
structure is an oriented biextension, and its height agrees with the higher
archimedean height pairing introduced in a previous paper by the first two
authors. We also compute a non-trivial example of this height given by
Bloch-Wigner dilogarithm function. Finally we study the variation of mixed
Hodge structures of Hodge-Tate type, and show that the height extends
continuously to degenerate situations.
