The problem of computing units in RHinfinity, that satisfy Ball-Gohberg-Rodman two-sided tangential interpolation conditions over the open right half complex plane is considered. We first show that every unit in RHinfinity can be written (up to left multiplication by an orthogonal matrix) as a finite product of positive real functions in RHinfinity with invertible value at infinity. This factorization is used to recast interpolation conditions on units as coupled positive real interpolation problems for the factors. An algebraic necessary and sufficient condition for the existence of solutions and a parameterization of all solutions (when one exists) are given. We introduce a multivariable parity interlacing property for left interpolation data and present an algorithm to compute units. The algorithm involves a line search and is guaranteed to terminate in a finite number of operations when the data set has parity interlacing property. As an application, strong stabilization of LTI plants is discussed. A procedure to construct a stable stabilizing controller is given. The results are illustrated with a simple MIMO example.