Either way it is a parliamentary system in which the executive is accountable to the body.
I like the idea of having something similar, and even though our executive is constitutionally on equal terms with the legislature there is nothing unconstitutional about requiring a formal interview session. Our Constitution already requires that the President address the Congress and the nation from time to time in the state of the union.
Its my understanding that under the Westminster system the body can force the executive to do something, while under our system Congress legally forcing the POTUS is rather rare. Adding an interview session with the Congress wouldn't change the formal balance of power, if anything it would act as a check against the runaway presidential power of the Modern Presidency.
Executive might not be the right word, the Prime Minister in the Westminster system is the head of government, not the head of state. The 'executive' would officially be the head of state, in the UK it is Queen. The Parliament cannot just force the Prime Minister to do something per se but they can actually vote them out without a general election, it happened to Thatcher in 1990.
And while some aspects are appealing one just has to look at Israel and Canada right now to see how minority/coalition governments can hobble a governments actions. While our system has some weaknesses it has a lot more strengths.