What type of a relationship does Eveline have with Frank?

The relationship between Eveline and Frank is in many respects a strange one. There is a suggestion that there's a difference in class status between the two, with Frank coming from a higher social background than Eveline. When Frank takes Eveline to the theater, for example, it's instructive that they sit in a section with which Eveline is wholly unaccustomed.
As well as disparities in income and class, there's an emotional gap too. There's no sense that Eveline is really in love with Frank, at least not very deeply. At best, she appears to see him as a means of escape from a drab, miserable home life. Yet even then, she's not so enthusiastic about the prospects of life with Frank as to up and run off with him to a far-off, distant country. At the same time, we can't say whether Frank has especially deep feelings towards Eveline, either. Perhaps he feels pity for her in some way; perhaps he sees himself as a knight in shining armour, saving a damsel in distress from the imprisonment of her daily life. We simply don't know for sure.
But one thing that we can say with a fair degree of confidence is that the uncertain nature of Eveline and Frank's relationship is reflected in their final parting, which, for both of them, hints at yet greater uncertainties to come.