Why does the ionosphere reflect HF but allow VHF signals to penetrate through?
Essentially it comes down to the fact that the ionosphere reflects different wavelengths differently.  To understand why we'd have to get into plasma physics but a short version is that the plasma characteristics are a function of density, species, ionization rate and ionization energy.  For certain wavelengths the ionosphere can interact with the wavelengths of the RF energy and acts like a mirror, at other wavelengths the frequency is such that the  ions don't interact as well and thus don't reflect the energy back.

Of course this is a coarse simplification.

This is similar to how you can have wavelength selective optical filters through interference effects.

Metals, which are typically shiny and mirror like, have their conduction band full of electrons which act as a sea of charge carriers which the light can interact with.  But even different metals have different Colors, which indicate a similar phenomenon to the ionospheric interaction.