Can the :before and :after pseudo-elements inherit height from the parent element?

No. The only way that pseudo-elements can inherit values from the parent of their generating element is when the generating element itself is also inheriting from its parent.

This is because inheritance occurs from a parent to a child, one level at a time. For inheritance to work across several levels of descendants, every descendant must inherit.

As an example, consider the following HTML:

<div class="parent">
    <div class="child">
    </div>
</div>

With the following CSS:

.parent {
    width: 100px;
    height: 100px;
}

.parent > .child:before, .parent > .child:after {
    content: '';
    position: absolute;
    width: inherit;
    height: inherit;
}

This will not work because even though the pseudo-elements have values of inherit, the element generating them, that is, .parent > .child, does not inherit from .parent. Instead, they inherit the default value of auto for both properties.

In order for this to work you will need to have .parent > .child inherit as well:

.parent {
    width: 100px;
    height: 100px;
}

.parent > .child {
    width: inherit;
    height: inherit;
}

.parent > .child:before, .parent > .child:after {
    content: '';
    position: absolute;
    width: inherit;
    height: inherit;
}