How the Dutch do it

We are a Dutch-British couple living in Netherlands. We want to visit China for 2-3 weeks. We both need a visa for that. Due to my partner needing his (British) passport (to enter work), we can't just send off his passport. This is not such a big problem for me, as I have a Dutch national ID card too.

Well, this sums it up quite nicely. Since your partner does need that specific passport it can't be sent away. You on the other hand, do not have that problem because you have a national ID to use in the meantime.

The tricks seems to have been there all along, your partner needs an extra form of identification. If I understand it correctly, your partner needs this specific passport in the meantime. Since you'll need a passport to go to China, a national ID card won't suffice. Instead, a second passport would.

This isn't super easy, but it's not impossible either. What you need is a good reason for needing a second passport. Now, the reason your partner needs their passport in the meantime might be a good enough reason, but it's not tried and tested.

A tried and tested reason for getting a second Dutch passport is travelling to different countries that are in some conflict. For example, travel to Israel and Palestine is a valid reason (for Dutch nationals) (because it may lead to additional questioning at the border).

The situation may arise that your first passport contains stamps from countries in conflict with the countries that you need to visit. This can cause problems when trying to enter those countries. A second passport could be the solution.

source: The Hague Municipality

How the Brits do it too, but more inconveniently

In your partner's case, we need a second British passport (assuming that's their only nationality). I cannot find a UK government source on this, but multiple blogs do mention the same reasoning as the Dutch.

I should note that that does mean making some extra travel plans. While I cannot advocate making plans and presenting them to an official to get official documents and then not using them for the reasons given, I don't think they will check afterwards.

boardingarea.com has a blog on this. I'll quote the relevant steps but note that the article linked is much more extensive:

Broadly speaking you will need to encounter one of the following two situations to convince the Her Majesty's Passport Office to issue you another UK passport:

[...]

1. You are a business traveller who needs to visit countries that are in conflict or incompatibility with each other, e.g. Israel and Iran/Lebanon/Syria/Iraq etc.

[...]

You can apply by post inside the UK, outside the UK , or at one of the passport interview centres.

[...]

In all cases, be sure that you are choosing the option to “Apply for a 1st adult passport”, and specifically request not to cancel your existing passport. If calling by telephone the operator should be aware of the process for business travellers obtaining a second document.

As this is a ‘1st passport application', they check your proof of UK citizenship with extra rigour. Depending on the nature of how you became a UK citizen (e.g. by birth or by naturalisation), the Passport Advice Line can advise you on what supporting evidence of your citizenship you need to bring to your appointment or submit by post. Normally this will include any one or more of the following documents:

• Your current UK passport – This is the easiest option if your name has changed since birth or issuance of other accepted certificates. See below.

[...]

In addition to the normal passport application form, passport photos signed by a person of good standing who has known you for at least 2 years, and the correct fee, you need to justify why you are requesting a second passport. This will mean showing detailed travel plans which causes you to request second passport. E.g. flight confirmations/tickets.

You will also need a letter on headed paper explaining your circumstance that is dated no earlier than 4 weeks prior to your application. I have adapted a template that I found on a forum post in Business Traveller which you will need to edit to suit your individual needs:

[...]

Perhaps easier for some Brits: become Dutch

If you're already living in the Netherlands, it might make sense to consider becoming a Dutch citizen so you can apply more easily for a second Dutch passport. How much easier this is will depend on your personal situation (see the long list of exemptions on the linked page), but I think it's worth mentioning.