A very good question! Essentially, usage differs according to register, so that, while in informal, conversational usage, ‘as well as’ is normally treated as a phrasal preposition, giving e.g.
Peter knows what is happening, as well as me.
(= Peter knows, and I know…)
in formal usage, many speakers will prefer to use it (in accordance with its syntactic origins as an elliptical comparative) rather as a phrasal conjunction, giving e.g.
Peter, as well as I, knows what is happening.
(< as well as/to the same extent that I know…)
the position of the phrase being also variable (sometimes for reasons of euphony).
However, when collocating with a following verbal structure that is not automatically deducible from context (as in the case of your problem sentence), the expression has become obligatorily elliptical, so that we cannot grammatically/meaningfully reinstate a putative full form
*We will mark their scripts as well as we will provide comments by highlighting their mistakes.
In such cases, consequently, the prepositional reading of ‘as well as’ naturally prevails, yielding therefore either (on the typical model of [preposition+Ving]) the gerund form as well as providing or, alternatively (on the special model of [besides+V]) as well as provide (the latter being, in fact, preferable here on account of the infinitive form ‘mark’ earlier in the sentence).