Polite language vs Casual language


The following is from a wedding invitation:

>
> このたび私たちは結婚式を挙げることになりました。つきましては日々お世話になっております皆様方をお招きしてささやかですが小宴を開催したいと存じます。ご多用中誠に恐縮ではございますがぜひご出席をいただきたくご案内申し上げます。敬具。

I have a particularly hard time understanding what 申し上げます means in the last
line:

> ご多用中誠に恐縮ではございますがぜひご出席をいただきたくご案内申し上げます。

From my understanding, there is a form of speech that is used to express
respect to someone (for example a boss), but there is also a form that lets
speakers humble themselves. I believe that in these forms, some verbs can be
interchangeable solely looking at the meaning (I only know about 存じる vs 知る).
Is 申し上げますa part of one of these forms? Which verb can it be interchanged with,
if any?

