Yesterday I already have tried to answer your question (role of Q2 and why pnp?), however some forum members heavily disagreed. I understand that you feel confused now - and, therefore, I think it is best for you to draw a picture of your own.
For this purpose, in the following I have listed some references, which may be helpful:
1) R.C. Jaeger, Microelectronic Circuit Design: "Alternating npn with pnp transistors from stage-to-stage is common in dc-coupled designs"
2) Sedra and Smith, Fig. 7.43, 7.44, 7.49
(„..the pnp transistor provides the essential function of shifting the dc level..“.)
3) Univ. of Berkeley: (pages 5...7 ): „By using complementary devices, active level shifting can be combined with amplification“.
(„By using complementary devices, active level shifting can be combined with amplification“)
5) Carleton Univ, Calif.: Fig. 12-11
6) Mass. Inst. of Tech.
http://ocw.mit.edu/resources/res-6-010-electronic-feedback-systems-spring-2013/textbook/MITRES_6-010S13_chap07.pdf Fig. 7-21
(identical to Roberge: Operational Amplifiers, p.280)
7) Ferranti Semiconductor (March 1974), (picture given at the top).