I have been taught that 'th' and 'ch' were pronounced just like 't' and 'c' in classical Latin, with no aspiration. The answer to this earlier question confirms that 't' and 'c' had indeed little or no aspiration. But did 'th' and 'ch' really lack aspiration as well? Was there any distinction between 't' and 'th' or 'c' and 'ch'?
The combinations 'th' and 'ch' mostly appear in Greek loan words, but for example pulcher is — as far as I know — not a Greek loan. The corresponding Greek letters θ and χ were aspirated, and I have understood that aspiration was a way of showing of high education, not a widespread feature in Latin pronunciation.
In some rare cases aspiration is called for, like in Catullus' poem to Harrius. There one needs strong aspiration to make a difference between commoda and chommoda. Rare examples like this do not necessarily imply that every occurrence of 'ch' and 'th' is aspirated.