It is obviously not a progressive (continuous) construction, since there is no -ing form (present participle) present.
It looks like a perfect passive construction, HAVE + BE + past participle; but it's not. Interested is a ‘participial adjective’—a past participle employed as an adjective, with its active verb sense ‘bleached out’—and in your sentence it acts as the predicate complement to the verb, which is the present perfect construction with BE, have been. Interested is not a verb designating an action performed on me but a adjective designating a quality which describes me, just like any other adjective:
I have been happy to meet new people.
I have been curious about his opinions.
I have been interested in electronics.
Note that the present participle of interest, interesting, also usually has adjectival force:
Electronics is interesting.
This is not a progressive construction: "interesting" is a quality attributed to the subject rather than an 'action' performed by the subject.