We're nerds. I've met very few Lib dems who aren't nerds. And some of us are nerds about transport, and some of us are nerds about budgets, and so on. That is who we are above all else. We're ravenclaws. (With some hufflepuffs). We write long complex policies with painstaking research only to have the other parties nick them, and then say "well at least the clever thing I designed is happening even if I don't get the credit".
Now, one thing we did with the coalition was do exactly what we'd been saying before the election. It wasn't what the media reported, but it is what we said. Which was that we'd consider coalition with any party that got the most votes and the most seats. Which was the Tories.
Now, you should also remember that the Lib Dems have a shared history with both the conservative and labour parties. The SDP may be much more recent, but the flight of the libertarians in the 1920s and 30s (along with the telegraph newspaper) lost us what was an originally liberal idea: the market. Suddenly we were no longer the party of the market. And the Tories were a mixture of market purists, capitalists and moral conservatives (political theists). They've purged most of the moral conservatives now, and we're just left with the capitalists (the libertarians forgot all about the social conscience of Adam Smith without the rest of the Liberal party to remind them.)
Now, the Liberals who were left in the 40s and onwards were several things. Social liberal, internationalist, a little bit CND, etc. Radicals. Protestors.
Then we got this influx from Labour in the 80s, the right wing of the Labour Party, the SDP. Vince Cable. Shirley Williams. We grew up and became less of a protest party and more professional. We started winning by-elections and having more than 6 seats.
It is important to distinguish us from a European Liberal (centre-right) party. It is also important to remember that we're internationalists. And it is important to remember that we're not too different from a European Liberal party; we definitely believe in free trade across borders.
So, the European project is a part of British Liberalism which cuts across both internationalism and market freedoms. It's in the political DNA of nearly all Lib Dems.
Brexit is one of the few things we pretty much all agree on (that it's a terrible catastrophe).
I hope that helps you understand us a bit better.