It is perfectly fine for a Western Catholic to participate in a Catholic Eastern-rite Liturgy, though one must be sure that it is truly Catholic, celebrated in communion with the Holy See.
By the way, “hearing” Mass is not an adequate idiom for our participation in the Eucharistic liturgy. To hear is to be passive, and we are meant to participate actively in the Mass. We are invited to unite ourselves with the Lord in his sacrificial prayer to the Father. When the priest says, “Through him, with him and in him, in the unity of the Holy Spirit, all glory and honor is yours, almighty Father, for ever and ever,” the faithful answer, “Amen.” That Amen makes Christ’s prayer ours as well.