Honor Doesn't Always Mean Obedience

Helena in A Midsummer Night's Dream is squarely comparable to Helena in All's Well That Ends Well in a number of ways, and a similar parallelism exists between Hermia and Innogen in Cymbeline.  From the viewpoint of the Hermia and Innogen, I think Cymbeline is a valid parallel. On the other hand, I don't think King Cymbeline and Egeus are very comparable. In Act I of A Midsummer Night's Dream, Egeus, Hermia's father, says:

Full of vexation come I, with complaint
Against my child, my daughter Hermia—
Stand forth, Demetrius.—My noble lord,
This man hath my consent to marry her.—
Stand forth, Lysander.—And, my gracious duke,
This man hath bewitched the bosom of my child. (I.1.23-28)

In Act I of Cymbeline, we get a taste of the king's opinion about Posthumus:

Thou basest thing, avoid hence, from my sight!
If after this command thou freight the court
With thy unworthiness, thou diest. Away,
Thou'rt poison to my blood. (I.1.126-129)

More like King Lear than Egeus, Cymbeline points blame to Innogen. Even Cymbeline's language suggests his difference from Egeus; Cymbeline is angry at his daughter, of course, and the above lines mirror closely King Henry IV's soliloquy in relation to his son in King Henry IV, Part 1, in which he portends, "He'll breed revengement and a scourge of me..." (III.2.7). Egeus, to the contrary, continues his tirade to place further blame on Lysander for Hermia's preference rather than to place blame on his daughter.

The primary parallel between Hermia and Innogen is their concern with propriety and honor.  In Cymbeline, Posthumus explains Innogen's purity to the courtiers in Italy: "Your Italy contains none so accomplished a courtier to convince the honour of my mistress, if in the holding or loss of that you term her frail. I do nothing doubt you have store of thieves; notwithstanding, I fear not my ring" (I.4.90-94). Hermia's own words and actions briefly reflect her own honor:

Now much beshrew my manners and my pride
If Hermia meant to say Lysander lied.
But, gentle friend, for love and courtesy,
Lie further off in human modesty.
Such separation, as may well be said,
Becomes a virtuous bachelor and a maid.
So far be distant; and good night, sweet friend. (II.2.60-66)

 In short, in spite of the ample ground for those wishing to contrast the two characters, in terms of character type, Hermia and Innogen are an excellent parallel between A Midsummer Night's Dream and Cymbeline, and analyzing this parallel can deepen understanding with regard to Hermia's character. This specific point of comparison highlights Hermia's dedication to Lysander, which is not a point I noted when reading the play initially.