Strange VIH and VIL specification of MIC4451
This is, in my opinion, a confusing usage of the terms max and min. What they're saying is that the minimum voltage you should apply to an input that you want to drive high is 2.4V, but a typical device will read anything down to 1.3V as high--it's just not guaranteed.

Likewise, the maximum voltage you should apply when driving a signal low is 0.8V, but typical devices will interpret up to 1.1V as low.

It does feel backwards to me, too; you're not alone in that.