She was relieved because Jonathan wasn't crazy after all.
Jonathan wrote about his experiences in Castle Dracula, hypothesizing that Dracula isn't really human. When Mina read this account, she started thinking Jonathan went mad and she was scared about the man she just married. Therefore she gave the diary to Van Helsing, who said that everything in it was true. She felt relieved on one hand that Jonathan wasn't mad, but scared on the other about the truth.