How can I Serialize/De-serialize a Boolean Value from FasterXML\Jackson as an Int?

As Paulo Pedroso's answer mentioned and referenced, you will need to roll your own custom JsonSerializer and JsonDeserializer. Once created, you will need to add the @JsonSerialize and @JsonDeserialize annotations to your property; specifying the class to use for each.

I have provided a small (hopefully straightforward) example below. Neither the serializer nor deserializer implementations are super robust but this should get you started.

public static class SimplePojo {

    @JsonProperty
    @JsonSerialize(using=NumericBooleanSerializer.class)
    @JsonDeserialize(using=NumericBooleanDeserializer.class)
    Boolean bool;
}

public static class NumericBooleanSerializer extends JsonSerializer<Boolean> {

    @Override
    public void serialize(Boolean bool, JsonGenerator generator, SerializerProvider provider) throws IOException, JsonProcessingException {
        generator.writeString(bool ? "1" : "0");
    }   
}

public static class NumericBooleanDeserializer extends JsonDeserializer<Boolean> {

    @Override
    public Boolean deserialize(JsonParser parser, DeserializationContext context) throws IOException, JsonProcessingException {
        return !"0".equals(parser.getText());
    }       
}

@Test
public void readAndWrite() throws JsonParseException, JsonMappingException, IOException {
    ObjectMapper mapper = new ObjectMapper();

    // read it
    SimplePojo sp = mapper.readValue("{\"bool\":\"0\"}", SimplePojo.class);
    assertThat(sp.bool, is(false));

    // write it
    StringWriter writer = new StringWriter();
    mapper.writeValue(writer, sp);
    assertThat(writer.toString(), is("{\"bool\":\"0\"}"));
}

Instead of custom deserializer, you could also simply have a setter like:

public void setThisIsABoolean(String str) {
  if ("0".equals(str)) {
    bool = false;
  } else {
    bool = true;
  }
}

since your method can claim different type than what you use internally.

And if you have to support both Boolean and String, you can indicate value is an Object, and check what you might get.

It should even be possible to have different type for getter method (Boolean) and setter (String or Object).