Is to be + verb-ing passive voice?

The essence of a passive construction is its framing of an idea so that the object of the action (the thing done) appears before the verb and the agent of the action (the thing responsible for performing the action) appears after the verb or not at all.

Here is an active construction:

Bozo the Clown made mistakes.

Here is a passive construction with the actor identified:

Mistakes were made by Bozo the Clown.

And here is a passive construction with the actor omitted:

Mistakes were made.

As a matter of style, one might prefer the directness and simplicity of "Bozo the Clown made mistakes" to "Mistakes were made by Bozo the Clown"; but from a reader's perspective, the latter describes the situation just as clearly as the former does. In contrast, "Mistakes were made" leaves the actor out of the account, which benefits no one but Bozo the Clown.

Unlike the second and third examples above, the following construction is not passive:

Bozo the Clown was making mistakes.

It is active because it places the actor or subject (Bozo the Clown) before the verb and the object or thing done (mistakes) after the verb. Your professor may not like constructions that use words of the form "was [verb]ing" or "is [verb]ing," but such constructions are not passive.

Your professor seems to have conflated the notion of "active" versus "passive" constructions with the notion of "weak" versus "strong" verbs. The latter nomenclature refers to a style preference (or irrational prejudice) against constructions that rely heavily (or at all) on verbs such as be, have, and do. Andrea Lunsford, The St. Martin's Handbook, fifth edition (2002) offers a typical criticism of "weak verbs":

The greatest writers in any language are those with a genius for choosing the precise words that will arrest and hold the reader's attention. In your own writing, you can help gain this attention by using precise nouns and adjectives instead of vague, empty ones [cross-reference omitted]. Perhaps even more important, however, you can use strong, precise verbs instead of weak, catchall verbs and instead of nouns.

...

Some of the most common verbs in English—especially be, do, and have—carry little or no sense of specific action, but many writers tend to overuse them in situations where more precise verbs would be clearer and more effective.

The "is having" wording that your professor specifically calls out would fall into Lunsford's "weak verb" category because it is built on a form of "have"; but your professor might well be under the impression that the "is [verb]ing" form—not the "have" element—is the chief indicator of weakness/passivity in the construction. It can be difficult for an outside observer to tell what rationale a person has used to reach a erroneous conclusion.

Of course, regardless of the terminology that your professor uses, you'll still have to go into contortions to avoid using "is [verb]ing" verb forms if you want to receive high marks on the papers you write for this class. But at least you won't use "passive construction" or "passive voice" incorrectly, as so many others do.