Well...

To begin, Let's look at the history of this "traditional" view of american politics.

First, the public trusting Republicans more on foreign affairs:This view only really came about since Korea, or perhaps a little before. I say perhaps a little before the Korean war because of the right wing canard that Roosevelt somehow knew of the Pearl Harbor attack, and let it occur. I don't think the reputable evidence lends itself to that conclusion. The point of the attack is that you cannot trust Democrats to defend the country because Roosevelt let us get attacked.

In the post war period, the Republicans had two competing viewpoints within their party. 1) The traditional conservative isolationism and 2) the desire to "confront" communism in a more aggressive manner, if for no other purpose than to beat up on Democrats who were then in power and whose New Deal policies appeared "red" to the far right. The "Democrats-can't-be-trusted-because-they-let-us-get-attacked" idea was used to discredit the crusading idealism of american intervention in the world that the left in america traditionally espoused. This led to the right attacking Truman, Kennedy, and Johnson with the two apparently contradictory strains of republican thought on foreign affairs. When Korea, and later Vietnam, turned into unwinnable messes, at least unwinnable in the traditional sense, (meaning we weren't going to get unconditional surrenders of our opponents in those wars) the right attacked the Democratic party for getting us into those messes in the first place, representing the traditional isolationism view. The right also attacked the Democratic policy makers for failing to "confront" communism more aggressively. The best examples here are MacArthur's insubordination against Truman and the later lies and attacks that we did not let the generals fight Vietnam the way they wanted to. This represents the second right wing viewpoint. As stated, as Korea, but really more importantly for recent politics, Vietnam, devolved into quagmire, the Republicans attacked the Democrats for the policy failures those wars represented, and argued that they, the republicans, could handle foreign affairs better. On the republicans' "plus" column was Nixon's trip to China and his draw down of forces in Vietnam. This idea repeated itself in the Iranian revolution and later hostage crisis. While I have done an exceptionally poor job outlining the history right now, I hope at least the skeleton is there for a future outline because the point is that these events led to the "traditional" view you describe, namely, that the public trusts the republican party more on foreign affairs.

As to the second point, that the public trusts the Democrats more on domestic issues, well that has really been the case since the Depression, and nothing the republicans have offered since then, except maybe tax cuts, ever garners much public support. My domestic policy analysis is WEAK. I cannot tell you why the public doesn't support the Republican domestic agenda, but they don't. If you, or anyone else can suggest a good book, I will put it on the reading list.

So having analyzed (hahaha because I didn't do any analysis on the domestic front, and there is so much more I could write on the international side) the history of those views, I agree it should be possible to develop a third axis. I think it is incumbent upon the Democrats to do that at this point. We are also uniquely suited to attack the Republicans in the same way they attacked us during the Cold War and Vietnam because this Iraq adventure (I hate doing that by the way, writing something so flippant about a place where our soldiers are living and, more importantly, dying right now.) is turning out to be a mess. We as Democrats and liberals need to develop an alternative foreign policy and attacks that we can use against the current idea that republicans are better at international relations. Iraq presents us with a unique opportunity to accomplish both those goals.

Now, what would this third axis look like? I dunno, we can discuss that more in the future.