In my dumbed-down, over-simplified, rule-of-thumb grasp of Church history and theology, I associate the term via media with John Henry Newman. He it was, I think, who, long before kicking the dust of Anglicanism from his Oxford brogues, used the term to describe the "middle way" between Puritan Protestantism and Roman Catholicism which was the Church of England's inheritance from the Elizabethan Settlement onwards. Newman himself believed - at that stage, anyway - that the Church had, during the 18th century, forgotten its ancient Catholic heritage enshrined in the Book of Common Prayer, and had in the process become a dull department of a Hanoverian Protestant state. He and his fellow Tractarians - who were to become the founding fathers of the Oxford Movement - fretted about Erastianism (the idea that the state should have authority over the Church in ecclesiastical matters) and worried that the Church of England was in danger of losing its identity, squeezed as it was between a newly restored and growing Roman Catholic Church and the vigorous Protestant sects that had grown during the evangelical revival of the previous century. With reference to the Early Fathers and the Elizabethan and Caroline divines, the Tractarians re-imagined the true English Church. This Church looked quite a bit more Catholic than it had done (and indeed than many were comfortable with) and effectively began what some regard as the recatholicisation of Anglicanism. The Oxford Movement begat Anglo-Catholicism - a term I believe also coined by Newman, and a movement which survived his defection to Rome and which profoundly influenced subsequent Church of England life and polity.
But Tractarianism did not want England to revert to Rome; it wanted the Church to recover what it had lost or deprecated but which was there in black and white in the pages of the 1662 Prayer Book - its liturgical and ecclesiological authority. This, they believed, envisaged much more frequent access to the sacraments (Newman's "keys and spells"), the most radical expression of which was perhaps their espousal of the restoration of auricular confession in the Church of England. But the "excesses" of Rome were not on the agenda, any more than were the radical claims and uncanonical practices of evangelical Protestantism. The Church of England was not a confessional denomination like Lutheranism; it was the liberated and reformed catholic (ie universal) Church of England. Seen from this perspective, the via media was not just a matter of advocating a moderate Christianity: it had been the Church's calling from the beginning.
If I were a fundamentalist evangelical I would be expected to believe in some or all of the following: the Bible as the literal and inerrant word of God; the claim that He created the world in six days about 6000 years ago; that ordained priesthood is at best unnecessary (and that when the Bishop put his hands on my head, nothing happened beyond his spoiling my hair-do); that the bread and wine of the Eucharist are merely symbolic; that the dead are dead and beyond my prayers; that some are predestined for salvation and that the rest are irretrievably doomed; and that the Church on earth is no more than a convenient way of organising Christians.
If I were a Roman Catholic I would be obliged to believe: the notion that a human being, however wise and holy he might be, is infallible (when speaking ex cathedra but not otherwise); that it is possible for that same person to arrange for me to spend less time in purgatory in return for my attendance at a service or event; that belief in the "immaculate" conception and bodily assumption of the Blessed Virgin Mary are necessary to my salvation; that a prayer to a native Canadian woman who died in 1680 recently and miraculously cured a little boy of a fatal disease, warranting her canonisation last year; and for good measure, that my church is not a church at all, and that my holy orders are "absolutely null and utterly void".
As it is, I am free to believe any or all of these things - but not obliged to. (It would actually be rather odd if I believed the last of them, but some Anglican priests are doing just that in respect of the so-called "Ordinariate".) It is probably good for me to make my confession to a priest, but my salvation does not depend upon it. If I believe that the substance of the bread and wine of the Eucharist is changed by their consecration, I may so believe entirely legitimately, but may not insist on the same belief on the part of my fellow-worshipper.
For occupying this middle ground, and notwithstanding my decidedly illiberal credal orthodoxy, some will accuse me of being a wishy-washy fence-sitter, and/or a milk-and-water relativist. Others will conclude simply (and perhaps sadly) that I am going to hell in a handcart and that there is no help for me unless I repent of my wilful rejection of the truth. Well, they may or may not be right. As it is, I count myself rather fortunate not to be obliged to adhere to dogma which I find ridiculous while keeping it to myself. I belong to a Church and Communion which does not invite people to sign up to any theological propositions beyond those "uniquely revealed in the Holy Scriptures and set forth in the catholic creeds", but which says to them merely: "We are your church. This is what we do. Can you worship with us?"