Assuming you don't need the verbatim to be highlighted you could use a 
span with a custom style instead of a Code element, and define that 
custom style however you want (search for "custom-style" in the manual!):

``````markdown
# The [switch]{custom-style=H1-verb} keyword
``````

Since that custom style attribute is a lot to type I would probably use 
a combination of a class and a Lua filter, especially since the heading 
text in Markdown has to fit on a single physical line, and so that it 
doesn't break if I change the level of a heading:

``````markdown
# The [switch]{.hv} keyword

## The [ref]{.hv} and [out]{.hv} keywords

### The [far]{.hv} and [near]{.hv} modifiers

#### The [printf()]{.hv} function
``````

and then in "header-verb.lua":

``````lua
-- Template for custom style, where %d will be filled in with
-- the heading's level number
local style_template = 'Heading %d Verbatim'

-- Filter generator for walking a header and fix spans
local function mk_span_filter (level)
   style_name = style_template:format(level)
   return { Span = function (span)
     if not span.classes:includes('hv') then return nil end
     span.attributes['custom-style'] = style_name
     return span
   end
}
end

function Header (head)
   local filter = mk_span_filter(head.level)
   return pandoc.walk_block(head, filter)
end
``````

Then in your reference DOCX define the "Heading 1 Verbatim" "Heading 2 
Verbatim" etc. styles, presumably as inheriting from "Verbatim Char" as 
you wish and you are good to go.

An irritation is that you apparently can't override bold/italic set in 
the paragraph style, at least in LibreOffice.

Files attached.  Tested with pandoc 2.9.2 and LibreOffice 6.0.7.3



On 2020-08-06 22:17, Anton Shepelev wrote:
> I asked:
> 
>> As  distinct  from  other  Markdown processors and
>> other output formats, while rendering DOCX  output
>> with  Pandoc,  inline  `verbatim`  text in headers
>> does not work so well, because it inherits not on-
>> ly  the  font,  but  also  the  font size from the
>> `Verbatim Char' style. I do realise that it is the
>> right  thing  to  do for running text because most
>> monospace fonts look  better  at  a  slightly  de-
>> creased  size  (e.g. 12pt Times New Roman and 11pt
>> Courier New), but I still should like to see  nice
>> typewriter text in headers:
>>
>>               ## The `switch` keyword
> 
> I wonder who nobody replied.  What is your method of
> typsetting such headers:
> 
> # The `switch` keyword
> # The `ref` and `out` keywords
> # The `far` and `near` modifiers
> # The `printf()` function
> 
> Do you fix them in your Lua filters?  Is  it  better
> to  have  this  functionality in a Lua filters on in
> Pandoc itself?
> 

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