Welcome to Wefugees and thank you for your question!
Firs of all: if you two intend to get married in Germany, your boyfriend will need a passport first - it is one of the core requirements to get married in Germany. Recognized refugees receive a "passport for fugitives"/ travel document by the local Immigration Office (usually with the residence permit) that is often referred to as the "Blue Passport".
Please note that recognized refugees are not permitted to obtain a passport from their country's embassy or travel to their country of origin, otherwise they may lose their protection status!
This is a Wikipedia article (translated), but it explains what the travel document for refugees is and where you can travel to: https://translate.google.com/translate?sl=de&tl=en&js=y&prev=_t&hl=de&ie=UTF-8&u=https%3A%2F%2Fde.wikipedia.org%2Fwiki%2FReiseausweis_f%25C3%25BCr_Fl%25C3%25BCchtlinge&edit-text=
Otherwise, please have a look at these threads from our platform:
Am I allowed to travel Europe as a refugee?
I am going to Spain, is there any problem?
Do I need a visa to travel to Newcastle/England?
As you can read on the last thread, travel restrictions apply to the UK, so he would need a visa - and I assume Brexit will change the situation to some extent as well.
Regarding your marriage, here is an article from our Wefugees Blog on "How to Marry" in Germany (please scroll down for the English version): https://wefugees.wordpress.com/2018/04/20/heiraten-in-deutschland-how-to-marry/
I hope this information helps! Please reach out to us again if you need any further assistance or have more questions :-)