The petit bourgeoisie and the haut bourgeoisie are both capitalist classes, though the petit bourgeoisie is a hybrid capitalist class (in the traditional formulation, dependent on ability to apply their own labor to their capital in order to live without liquidating capital [0]) rather than a pure capitalist classs like the haut bourgeiosie. And while the petit bourgeoisie is a “middle” class in the sense of being situated between the proletariat and the haut bourgeoisie, both bourgeois classes are “upper” classes in the sense that in capitalist society they together represent an elite minority of the population, most of which working class.

The sense in which they are a “middle class is quite distinct from the usual American sense of “middle class” which is usually an income-defined band centered around median income which is overwhelming part of the working class in the scheme in which the petit bourgeoisie are the “middle class”.

[0] But I think most people who use the scheme now would recognize more diversity, including the form probably most common to modern white-collar professionals, where rather than applying their own labor to their own capital, a lot of the petit bourgeiosie both rents labor out to other capitalists in the manner typical of the proletariat and has capital to which rented labor is applied in the manner of the haut bourgeoisie, with both being significant to their interaction with the economy (distinguishing them from workers with incidental capital holdings or capitalists who incidentally have a “paid job” which they could take or leave without meaningfully impacting their lifestyle or overall engagement in the economy.)