Learn English – Word like “serendipity” but with less emphasis on fortune or development of events

Fond can be considered as more than like and less than love. (Used as be fond of)

Having a strong liking, inclination, or affection: fond of ballet; fond of my nieces and nephews.

^{http://www.thefreedictionary.com/fond}

Though, it might depend on the context and it can be synonymous to like also. It is usually not used in a romantic relationship and you can both love and be fond of someone. For example, you can both love your niece and be fond of him because you like to spend time with him.

Other than that, infatuation can be considered as an early stage of a true love (used as infatuated with) but it is not necessarily between like and love. It is called puppy love also.

For example, an urbandictionary entry says:

Infatuation consists of people thinking they are in love but when indeed it is just a deep lust or like for another person.

Also, attraction can be stronger than like and weaker than love. (used as attracted to). Though it is usually a physical attraction and you can be attracted to someone you don't like. (an emotional irony?)

In the end, it might be better to use several words to explain the emotion than using a single word that might not be enough. There are different situations and contexts.

In my book

It might not always fit what you're trying to express, but should do most of the times. (I would also like a better answer.)

Examples:

In my book, if I lend you something, I should not have to ask for it back.

And to quote Google Definitions, that counts as a lie in my book.