A word that means a pseudo joke that has underlying meaning

Example 1

Yesterday, I had a conversation with my roommate regarding the possibility of getting a workbench.

She remarked:

If this is anything like the whiteboard, you'll just take it over completely.

I responded in a slightly defensive manner to which she retorted that she was "just joking". I acknowledge that there is truth in what she said because I have used the whiteboard a lot and I think she took the chance to convey this to me in the form of "a joke".

Example 2

Imagine a conversation amongst two friends: Waldo and Enrique.

Enrique: Waldo, do you know why you can't find a girlfriend?

Waldo: Not this again.

Enrique: My friend, it's because you smell as bad as you look.

Waldo: I don't smell!

Enrique: Of course, I'm just joking my friend. Let's get a drink.

Example 3

Imagine a child who wants to admit their feelings to a parent, but out of embarrassment they add the just kidding clause.

Example 4

Imagine a man (Carter) working at an office and he is having a conversation with the CEO of the company (Candice).

Carter: How did the presentation with the customers go?

Candice: It went alright, but there are still a lot of concerns to deal with.

Carter: That's too bad. * puts pen down on desk, stands up and exclaims * I have an IDEA!

Candice: Let's hear it!

Carter: You should promote me and then we can lead this company to world domination!

Candice: Oh lord. Sit down Carter, I should have guessed.

In this example Carter made a joke, but did not add the just-kidding clause. However, the important point here is that the joke has the underlying meaning--he wants a raise.

Background

This phenomenon is the reason behind the phrase: There's a grain of truth in every joke

Many articles talk about this, but I haven't come across a word for this. Pyschology Today has a good article about this, but doesn't have a name for this.

Sarcasm is probably most often referenced for this because most examples involve hurtful/negative sentiment; however, these pseudo-jokes are not limited to contexts with negative sentiment. In a deeper sense they are related to underlying desires that people want to subtly convey (see example 3 & 4).

I would like to add that I believe Sarcasm is more common in this respect because it is easier to pull off a joke in negative context rather than what is in example 4 (at least in Western culture).

I'm looking for a colloquial word or phrase that describes this type of joke.

One common name for this is "kidding on the square." When people are kidding on the square, they are joking, but also really mean what they're saying.

http://www.allwords.com/word-kid+on+the+square.html

The Jargon File mentions the phrase ha ha only serious:

[from SF fandom, orig. as mutation of HHOK, ‘Ha Ha Only Kidding’] A phrase (often seen abbreviated as HHOS) that aptly captures the flavor of much hacker discourse. Applied especially to parodies, absurdities, and ironic jokes that are both intended and perceived to contain a possibly disquieting amount of truth, or truths that are constructed on in-joke and self-parody.

Another possibility is being ironically sincere: using the trappings of irony, which seem to imply you don't mean what you're saying, to convey a message that's actually sincere. This could also be called meta-irony, although Marcel Duchamp used that phrase to refer to something different.

It's a barb - an insult disguised as a joke.

Macmillan:

barb
NOUN [COUNTABLE]
a remark or criticism that is unkind, although it may seem clever or funny