She is a noblewoman, and expects to be treated as one.

Literal

She [topic-は] noblewoman [is-and-であり], that-kind person [as-として] be-treated [thing-もの-と] thinks.

Three notable patterns layer here. であり is the formal continuative form of だ — equivalent to で (te-form of だ) but more written, used to chain clauses in essays and formal narration. ~として ('as, in the capacity of') marks role or status. ~ものと思う is a fixed locution meaning 'thinks/expects (as a matter of course)'; もの here adds an air of self-evident expectation, of 'naturally one would think.' The phrase そのような人 ('that kind of person') refers back to 貴婦人 just stated, like English 'such a person.' The whole sentence reads as a portrait of imperious self-regard.